Unpredictable weather

Today, during my Chinese class, I heard the rumbling of thunder. I thought it might rain. Although the rainy season has already finished in Taiwan, we sometimes have showers in the evening. Just as I thought (I was right!), I found(?) *1 it rained after class. But fortunately, it only rained a little, not showers. So I hurried home. Heavy rain is so annoying because it makes my clothes/my clothes get *2 totally wet!! I was relieved that I was able to get home without getting wet.
It’s hard to predict the weather in Taiwan (The weather in Taiwan is unpredictable) *3, so I have to bring a folding umbrella with me every day. And I like jogging, so the timing of my jogging/jogging before it starts raining *4 is important. How about the climate in your country?

* 1 "I found it rained after class" sounds strange but not because it's wrong. It might be British English which is why I'm unfamiliar with it, but personally I would just omit this part. The "I found" sounds like a shorthand way of saying "I found out" (found out: discovering/learning something surprising/on the contrary either on your own or after being informed by someone else) which seems like an odd thing to say here.
* 2 "It makes my clothes totally wet" isn't wrong but "because my clothes get totally wet" is a little more natural in my opinion.
* 3 The part you put in parentheses isn't necessary since you're essentially just saying the same thing twice. You can use either of the two sentences you wrote, but saying it twice is redundant.
* 4 "So the timing of my jogging is important" isn't wrong but it sounds a little odd. "So jogging before it starts raining is important" sounds more natural.

Edo movies

About 150 years ago, the revolution called "Meiji-ishin" occurred* 1 and after that Japan was modernized very quickly.
Before that, the Japanese life style was quite old-fashioned. We hadn't used electricity nor steam engines. Japan was in its Medieval Age until only 150 years ago.
We call this age the "Edo era" or "Tokugawa period".
I like the Edo era very much.
It is very fascinating.
If time machine is invented I want to go to Edo era/If I had a time machine I would travel back in time to the Edo era*2.

I love watching dramas and movies that are set in the Edo era.
Although they are now making very less much fewer *3 dramas of the Edo era than before.
When I was a child, we had about ten Edo dramas in on the air(?)*4 a week but now we have only one or two.
It's too bad a shame.
The reason of that/for it *5 seems to be that that it costs much more money than for modern movies.
They need some knowledges *6 to shoot Edo dramas and movies. It must be passed down to the next generation. I want them to keep making Edo movies.
If they stop making Edo movies at all entirely *7, the knowledges *6 will go extinct forever and we can never won't get to see new Edo movies anymore.

I don't want it to happen.

* 1 "The [something] revolution occurred" isn't incorrect but it has a slightly negative tone to it, which is fine in this case since you like the Edo period. Though if you want to sound a little more natural you can change the wording to "the Meiji-ishin revolution occurred" by removing the extra "called" and swapping Meiji-ishin and revolution around.
* 2 There's nothing wrong with what you wrote, it just sounds a bit strange. When we talk about what we would do if time machines existed, we usually say "if I had a time machine I would [...]" which is more natural.
* 3 "Very less" is incorrect. You can change it to simply "less" but if you want to stress that there are not nearly as many as before you should say "much fewer."
* 4 The way this is worded makes it a little difficult to understand exactly what you meant and it could be interpreted as 10 whole dramas being scheduled each week. I'm assuming you were talking about TV dramas, so in this case "on the air" (meaning that 10 different shows are airing in the same period of a week, not necessarily that they are shown in their entirety in a week) is more natural. The expression "on the air" means a show is being broadcast; the signal which you need to watch it travels through the air, so you could say the show is "on" the air.
* 5 "For it" makes the intended meaning a bit more clear and sounds more natural than "of that."
* 6 "Knowledge" is an uncountable noun, meaning we always say it in its singular form. Furthermore, in the first example, I think replacing this word with something else would make just what they need more clear. They might need a historian, a whole crew of people who can make authentic costumes, and so on. You could also say "they need to know a lot about the Edo period to make a drama of it" which works just as well.
* 7 "At all" is not correct in this case. You could say "altogether" or "entirely."

My PC is now really working well

I made some entries about my PC trouble yesterday and in the last one I wrote it was working well somehow.
Although the next day, the trouble began happening/it started acting up* 1 again.
It has broken many times since I built it. I repaired it every time it broke.
I was sick of repairing and thought about buying a new one.

I suppose I was upset a bit at the time so I couldn't cope deal *2 with it properly.
There would could still be something I could do before I decided to buy a new PC.

However the trouble came to happen again and this time this time when it started acting up *1, I could keep calm and thought that I would try to figure out what was causing this trouble/the issue *3.
Then finally I found it.
The source of the trouble problem *4 was the temperature rise of the CPU as CPU's temperature getting higher than *5 I expected once.
I set some values relating to the CPU a bit lower in the BIOS screen then the trouble stopped happening *6.
Maybe what I shall should *7 do next is to get a better CPU cooler. Of course it is much cheaper than (buying) *8 a whole (new) *8 PC.
In addition to that, I think it is not necessary to change the CPU cooler since it is now working very well.
I am happy that I could save (some) *8 money.

* 1 Saying that "trouble [is/was] happening" is not incorrect but it sounds unnatural. A more natural phrase in this case would be "it started acting up." "Acting up" refers to something not performing as well as it could be, or that is malfunctioning.
* 2 "Cope" isn't wrong but cope is a bit of a strong word that we mainly use for getting over setbacks like losing a job, a divorce, the death of a family member or pet, and so on. "Deal with" means the same thing but is less intense in meaning. You can of course still say "cope" if this is what you meant and your computer having problems is an important matter to you.
* 3 In this case "the issue" or "the problem" are more suitable. You can say "what was causing it to act up" here as well though.
* 4 Same as above.
* 5 The wording was pretty strange here so I moved some words around and tried to correct it into what I believe what you meant while preserving as much of the original sentence as I could.
* 6 Again, "trouble happening" isn't wrong but it sounds unnatural. Here it sounds slightly more natural than in other instances though. You could say "it started working again" (focusing on the positive) or "it stopped malfunctioning" (slightly negative, but that's not necessarily bad) to sound more natural though.
* 7 Since you started the sentence by saying "maybe" it means you are not entirely certain, so "shall" should be "should." Shall = "I WILL do this", should = "it would be best if I did this, but I might not (e.g. maybe you don't need to.)"
* 8 All these words are optional but "buying" and "new" makes it more clear what you're talking about (it's not hard to guess, but with the extra words in place there's no need to guess) and the final "some" just sounds more natural. In English we use "some" a lot when we're describing an unspecified (as in not relevant to the conversation) amount.

News Translation

A record downpour hit the northern Kyūshū* 1 region, killing 18 people and injuring 14 in the Fukuoka and Oita prefectures.*2

九州北部を襲った記録的な豪雨で、福岡県と大分県ではあわせて１８人が死亡し、１４人がけがをしました。

* 1 This is not technically wrong since there are many ways (and none of them are standardized) to write Japanese in romaji, however in my experience the Hepburn Romanization system is the most commonly used. "Kyusyu" isn't wrong, but with the Hepburn system you write it like "Kyūshū." You can also write it "Kyushu" or "Kyuushuu" among many others (Kyushu being considered acceptable in spite of the fact Kyushu is written with a long vowel - uu, but people may not know how to make the ū character on their keyboard) but I thought it was worth mentioning this.
* 2 Since people were injured and killed in more than 1 prefecture we say prefectures.

Härliga Sverige

Nu har jag bott i Sverige i 3 månader. Jag har en massa *1 respekt för Sveriges kultur, regler och livsstil. Människorna här *2 är lunga lugna *3 och ärtiga artiga *3. Jag tycker *4 speciellt tycker(←) om hur alla är så väldigt aktiva och går ut i alla väder vilket väder som helst *5. Jag är glad att vara halvsvensk *6. En sak som jag önskar för är lite mer det fanns mer av är *7 aktiviteter liksom *8 att musik spelar spela musik, matprövningar (smakprov av mat) *9 och fester. Jag tycker att Spanien, Italien och andra europeiska lander gör ju *10 dessa bättre ;)

Usually I'd explain my corrections in Swedish because I believe exposure whenever possible is good for learning a language, but in this case you're making so many mistakes (not trying to be rude) that I think it would be harder for you to understand if I did so, so I will explain my corrections in English.

* 1 "Jag har massor respekt" is close but incorrect. (ENG: "I have lots respect") "Jag har en massa respekt" ("en massa respekt" literally means the same thing in English as "a lot (of) respect") is correct.
* 2 "Människor är lunga och ärtiga" is simply stating a fact and is doing so about all of humanity. (ENG: "People are kind and polite") "Människorna här" (ENG: THE people HERE) is correct.
* 3 You said "lunga" which is means "lung" as in the organ you use to breathe. "Lugna"(note where the g and n are placed as they change the meaning of the word entirely) is "calm/relaxed/easygoing/etc." "Ärtiga" means "pealike" - you meant "artiga" (polite.)
* 4 "Tycker" almost always comes after "jag"(/hon/han/etc.) so I moved it to the front.
* 5 "I alla väder" sounds a little strange. "Vilket väder som helst" (ENG/LIT: any weather possible, ENG/ACT: no matter the weather) is more appropriate.
* 6 "Half Swedish" is one word - halvsvensk - in Swedish.
* 7 "Jag önskar för lite mer" (ENG: I wish for a few more) (←my guess of what you were trying to say) sounds unnatural in Swedish. To express we wish there were more of something we say "jag önskar det fanns (lite) mer" (ENG/LIT: I wish there existed (a little) more) but to preserve your original sentence as much as possible I changed it to "En sak som jag önskar det fanns mer av är" (ENG/LIT: A thing I wish there existed more of is.)
* 8 "Liksom" is essentially a conversational filler, like "kinda," "you know," or "like" in English. "Liksom" literally means "like like" - taking both the like as in "he's like a brother to me" and the like in "like... I dunno" but its meaning in a conversation is the exact same as "sort of" (as in "he's sort of weird") in English.
* 9 "Matprövningar" isn't wrong but it sounds weird. "Smakprovningar av mat" (ENG/LIT: taste testing of food) is a bit more natural:
(Final 10th note will be in the comments, I ran out of space.)

Like Mitch said, the way -ei and -ou words are pronounced depends on how carefully you wish to enunciate it, particularly on its own. On its own, the word 丁寧, when trying to pronounce it carefully, is pronounced ていねい (with the "t" from "take" and the "ay" from "say," and "nay") but in actual conversations words such as this (in my experience they all follow this rule, for example ケイタイ、両方、工場、etc.) the first vowel is simply extended. In other words, ていねい becomes てーねー (with the "te" from "television" (but slightly longer, "teelevision") and the "ne" from "next" (but again a little longer, "neext")) and the same rule generally applies for -ou words as well - 工場 (こうじょう) has two -ou sounds that are technically pronounced with the "o" from "company" and the "u" from "ultra" but in actual conversations it is usually pronounced こーじょー。 Like Mitch said, we do this in English too. "Best friend" becomes "bes fren" in actual conversations. "Actual" (act-you-all) becomes "akshul" and "momentarily" (mow-men-tare-ily) becomes "momentearlee" and so on and so on. In short, you don't need to worry about enunciating it 100% accurately, because conversational simplifications like this happen in all languages. If some confusion occurs (because of homophones, perhaps) enunciating it more carefully might not work and you're better off using it in a familiar sentence (in English, if someone doesn't understand the difference between "no" and "know" you could say "the "no" in "no thanks" or "the "know" in "I know that already.")