Thank you for your responses, and I aplies; I'm always happy towhen I receive them. Thank you for your replies; I'm always happy when I receive them.

Thank you for your responses, and; I am always happy to receive them. Thank you for your responses; I am always happy to receive them.

I just published some pieces of my writing from back then. I just published some pieces of my writing from back then.

I just published some pieces of my writing back then. I just published some pieces of my writing.

It's not clear what "back then" is referring to (maybe "from before" (?)).

Sorry for misunderstanding you. Sorry for misunderstanding you.

This is a correct sentence, but it's without context.

Yes, I am very fond of communicating with you by sending each othervia messages. Yes, I am very fond of communicating with you via messages.

Yes, I am very fond of communicating with you by sending each otherexchanging messages. I am very fond of communicating with you by exchanging messages.

"Yes" has no context.

I know you can speak Chinese, but I don't know'm not sure that you can understand Chinese writing wellit when written. I know you can speak Chinese, but I'm not sure that you can understand it when written.

I know you can speak Chinese, but I doidn't knowrealize that you can easily understand Chinese writing well. I know you can speak Chinese, but I didn't realize that you can easily understand Chinese writing.

Although I know a bit of English, I'm still can't read English writingsnot able to read it well because I don't have a big Englishlarge vocabulary pool and dohaven't mastered many English phrases. Although I know a bit of English, I'm still not able to read it well because I don't have a large vocabulary pool and haven't mastered many English phrases.

Although I know a bit of English, I still can't easily read English writings well because I don't have a biglarge English vocabulary pool and don'tand am yet to master many English phrases. Although I know a bit of English, I still can't easily read English writing because I don't have a large English vocabulary and am yet to master many English phrases.

One thing I a'm curious about is what your mother tongue is,; is it Chinese or English? One thing I'm curious about is what your mother tongue is; is it Chinese or English?

One thing I am curious about is: what is your mother tongue is, Chinese or English? One thing I am curious about is: what is your mother tongue, Chinese or English?

If you don't mind. If you don't mind.

A softer way to phrase this might be: "If it's not too much to ask"

If you don't mind. If you don't mind.

Ordinarily this would be a "sentence fragment", basically an incomplete sentence, but it's understandable from the context.