Skating

I went <strike>to</strike> skating at <strike>c\</strike>Central park.
<You can say "went skating" or "went to skate">

I really enjoy<strike>ed</strike><strike> to</strike> skating. Long time since I've been skating.
<same here, you can "enjoy skating" or enjoyed skating. You could also say "It's been a long time since I've skated">

The skating rink was filled with a lot of couple. A lot of couples enjoyed skating. Hand in hand!!
<Here you can say it was filled with a lot of people or say "The skating rink was full" In your next sentence I would have said "There were a lot of couples enjoying themselves, skating hand in hand!">
The skating rink <strike>heared</strike> played some nice music.
<I'm not sure if you were trying to say that the rink played good music or you heard good music their. If you meant to say you heard good music write "At the skating rink, I heard some nice music">
<strike>There is</strike> It was such nice mood!!!

Next time, I want to go as a couple!! haha~

Walk in Taipei (3)

The Next day, I woke up at 6 a.m. Oh, how early I woke up !! I ordinarily don't wake up so early when I go to my office.
That day I was going to go to the National Palace Museum.
First, I went from ZhongShan station to ShiLin station, and I <strike>ride</strike> rode on <strike>a</strike> the bus to get to the museum. (It's correct to say rode on a bus, but you can take out the word on. =] I say I rode the bus. You can also take out "to get" and say I rode on the bus to the museum.)
The <strike>station of</strike> MRT station is similar to the metro station in Osaka in some ways.
Besides, the atmosphere of Taipei is very similar to the atmosphere of Osaka in <strike>all the</strike> every way.
The woman I saw the day before<strike>, She was</strike> looked like a person in Osaka. lol

In the train, the seats were less than one of Japan. (I'm not sure what you're trying to say here.)
But young people never <strike>sat on</strike> sit in the priority seats, even if there <strike>weren't</strike> aren't any old people around there.
They were also giving up to old people their seat which wasn't the priority seat. (Better: They also gave up their seats to old people, even though they didn't have prority seats)
(They called old people who stood remote place, and they gave up their seat.) (Better: They called to the old people who were standing alone and gave them the seats)
It's a pity that I don't see that <strike>scene</strike> in Japan very often. The Japanese must think it over, of course, including me.

Well, I got to ShiLin station and I waited for <strike>a</strike> the bus <strike>which went</strike> that goes to the museum.
I'<strike>ve</strike> felt uneasy, because I <strike>have</strike> had to ride a bus <strike>at</strike> for the 2nd time in a foreign country.
<strike>But</strike> Actually, It was very easy to ride <strike>a</strike> the bus, so <strike>it</strike> there was no need to be anxious.
While I was <strike>in</strike> on the bus, I experienced <strike>a</strike> something strange <strike>happening</strike>. (Better: While I was on the bus, something strange happened)
When the bus driver said something in Chinese (maybe about our destination <strike>and other things</strike> or something),<strike>then suddenly</strike> the passengers suddenly clapped their hands. (Better: the passengers suddenly started clapping their hands.)
<strike>For what</strike> Why did they clap<strike>ped</strike> their hands? What did the driver <strike>said</strike> say?? Should I do like them? (Better: Should I have clapped to?)
I experienced this <strike>in</strike> on the bus <strike>returned</strike> returning to ShiLin. But I have no idea at all what happened...Tell me what happened if anyone knows.

Anyway, I arrived <strike>in</strike> at the museum at last!! (Better: Anyway, I finally arrived at the museum!!)

So much thanks for him (Better: I'm so grateful for him)

How time <strike>flys</strike> flies!
Two month<strike>e</strike>s and my English training <strike>has been finished</strike> is over.
<strike>To my surprise</strike> I'm surprised that I've made <strike>a</strike> great progress in oral English I think.  (This sentence makes sense, but it sounds slightly off to me, I think it would sound better if you took out the "I think" bit because you already said that you're surprised.)
<strike>I'm very</strike> I've really enjoyed my study time <strike>on</strike> in his class.
He is our English teacher who is a boy <strike>form</strike> from Washington America (Better: Our English teacher is a boy from Washington America) Also, we usually specify if it is Washington state or Washington D.C.
He has black skin and a <strike>paire</strike> pair of big eyes and he often keeps a plait. (Better: He has black skin, a pair of big eyes ond he often keeps a plait.)
He is active and pure-hearted. <strike>Especially he is</strike> He was especially <strike>good</strike> apprehensive when I showed <strike>out</strike> my opinion by my poor English. (I understand what you mean by apprehensive, but it would be better to say understanding)
So much thanks for him.
Now he has been back home. (Did you mean Now he has gone back home?)
Best wishes for him and hope <strike>his</strike> everything goes well.

I'm not sure what your asking? I'll just explain the differences, I guess. Two is the number after one. It's used for counting. For example; I have two eyes. Double can be used to describe twice the amount. For example; A double scoop ice cream has two scoops of ice cream. It can also mean two of identical (or similar) things. For example; After being hit on the head, he saw double. Dual is most often used for describing something that has two dissimilar characteristics. For example; I have a Dual DVD and VHS player. Twin is used to describe two individuals born at the same time to the same mother. For example; My cousin Rita gave birth to twins. It can also be used figuratively to describe someone who looks very much like another. For example; He looked like he could be John's twin. A duplex is most often used to describe two homes that share a single wall. For example; I live in Unit B of a Duplex.