Today I had a trial lesson for 30 minutes. It was my first time taking lessons online, so I felt nervous about speaking and was worried about whether online lessons would go well. The teacher was gentle and generous enough to listen to my speaking even though I have stammered many times and made many errors in grammar while speaking.

We talked about where we live, my goal of learning English, her way of teaching, my major, my travel experience and so on. It was only 30 minutes but I had a great time. She said she would give me (/offered to give me) writing homework and check it if I want. That would also be quite helpful and worthwhile. Hopefully I'll have a lesson with her again soon. ( I want to write more, but I want to go to bed. It's 0:40AM 12:40 AM/12:40 at night/it's past midnight!! [You can also say 0040, but we don't usually say it that way, at least in America])

We usually say "I don't mind" when something potentially negative happens, but it doesn't make us upset. For example: - I forgot to return the book I borrowed from you! I'm sorry! - Oh, I don't mind! Bring it back whenever you like. - It's raining today, but I don't mind, I have an umbrella. "I don't care" has a broader meaning than "I don't mind." It means "this isn't important to me". I disagree with Mario a little - I think "I don't care" isn't always rude. You can usually use it in the same situations as "I don't mind", but it's more informal. So with a friend, I could say "Oh, I don't care! Return it whenever you like" and it would be okay. "It's raining, but I don't care", is also fine. BUT, "I don't care" can definitely be very rude! For example: - I'm feeling so sick today! - I don't care. or - It's my birthday! - I don't care. Obviously, that's rude. X)

Reading, Writing, Listening, and Talking

Speaking and listening to English is harder for me than reading and writing English for me. When I read something or write notes, I can take my time and think it over to consider with my dicctionary. Depending on the article, I think reading newspapers is a good way/one of the best ways to study English, because they are written with correct and polite formal(?) sentences. Though if it's on a topic that I don't know much about or a difficult topic with lots of technical terms, I can't understand at all, not even in Japanese (?).

Yet when I listen to someone talking, for example in the movies, TV shows or interviews, I can scarcely catch what they're saying. Because people speak so fast and they don't talk in sentences like I read in the newspapers, neither I don't do that I can't understand them (?). Even if they talk slowly, using short sentences, and I can hear what they say, I can't understand them because of the word combinations they use, particularly verbs and prepositions. I suppose that it can be tough in any language.

So far, everyday conversation is the most difficult for me. isn't it? [This sounds like ね？ or かな？ in Japanese, but we don't use "isn't it?" after a personal statment like this in English. Since you're talking about your own experience, you can't ask the reader to support your statement.　Maybe saying "I <em>guess</em> everyday conversation is..." instead would give you the tone you wanted to use.] Nowadays I can read and listen, as well as talk through the internet. I will keep learning languages, even though it takes a lot of time. (Since I can learn so slowly.)

Please correct this note. I want you to tell me every small things that you think is strange or unnaturally.
Thank you.

She is always beautiful. - No special meaning. She is always beautiful, every day. Always she is beautiful. - This sentence is incorrect. (Carjul is right, "always" comes after the verb "to be", and before other verbs.) She is beautiful as always. - She is beautiful (now), like she always is! ("Look at this photo of Angelina Jolie. She is beautiful, as always.")

I made a mistake! The second example should be "("That helps me. However, I wonder..." Ignore this if it's confusing, or feel free to ask me to explain better!

Yes, perfect!! Only the punctuation is a little wrong. "Thank you, Julie. That helps me; however, I wonder if I can use it naturally or not" is better. In English, if you use a comma (,) to connect two complete sentences, you also need a coordinating conjunction (for, and, nor, but, or, yet, so). If you tie them together without a coordinating conjunction, we use a semicolon (;). So "however" can come either at the beginning of a new sentence ("That helps me. However; I wonder...") or after a semicolon. And it has a comma after it! I hope that wasn't confusing. It's not a very important detail. Other than that, it was perfect. :-)