I see I missed one or two minor corrections, as I was focused on the more significant deviations from native English. Note that “mail” is non-countable, so we should say an “email” or a “message,” which is more precise anyhow.

Here’s another version, where, in addition to correcting mistakes, we improve the style, by using more “natural” phrases and combining sentences. Note that even though I improved the style, I still tried to remain faithful to your original version — that is, I didn’t rewrite it exactly as I would have written it myself. The idea is just for you to become familiar with some options for expressing yourself in English.

English speaking group.

First, I will remember to send you a message about Chinese characters, it’s just that I’ve been so busy that I have had no time to respond to you, teacher Phil. I am sorry about that and I will reply to you as soon as possible. :)

I recently joined a school sponsored club where I can speak English. Only around fifteen students are in the club, and most of them do not really want to be there, but only came because their teacher asked them to. I knew most Taiwanese students had stayed in their comfort zone for a long time (that last clause is a bit confusing to me — I’m not 100% sure what you mean), but I still felt sad when I encountered this situation in person. (Note that the last sentence should all be in one tense. I put it in the past, because the previous sentence was in the past, and I imagine they refer to the same time.)

Teacher Glenda is pretty nice, so I was very happy speaking English with her. Since she is always patient with everybody, no one ever feels bad while talking to her (Or “No one ever feels bad talking to her, since she is so patient with everybody). I really wish I could speak to her everyday.

Nice job, Miss Chén! Here are a few minor corrections, as well as some optional suggestions:

English speaking group.

First, I will remember to send you a mail which is about Chinese words. But I am so busy that (we say either "so... that" or "too... to") I have had no time to respond you, teacher Phil. I am sorry about that and I will reply you as soon as possible. :)

I recently joined a group held by school recently  (Better: I recently joined a school sponsored club). I can speak English there. The members are only about 15 students (or "Only around fifteen students are members). Most of them came unwillingly (Um.. were they forced? If not, I would say they came "grudgingly").  They came just because their teacher asked them to. I know most Taiwanese students have stayed in their comfort zone for a long time. But I still felt sad when I encountered this situation in person. Teacher Glennda is pretty nice. I could speak English happily in front of her. She is always patient with everybody. No one will feel bad while talking to her. I really wish I can speak to her everyday. The last three sentences, while grammatically correct as they are, would have more coherence if combined into one complex sentence.