Hi, there! :)

I'm quite new here. Since I'd like to improve my English skills, so I signed up here today.
Could  Would you correct my texts and suggest more natural expressions?

I'm a native speaker of Japanese and maybe I could help your Japanese!

Hi, there! :)

I'm quite new here.

This is correct, but "I signed up here today because I want to improve my English" is a bit more natural.

Since I'd like to improve my English skills, I signed up here today.

"Could you correct my notebook entries..." When we say 'texts', we usually mean SMS text messages. 'Text' can also mean a book. e.g. "Look at page 45 in the text"

Could you correct my texts and suggest more natural expressions?

I'm a native speaker of Japanese and maybe I could help your Japanese!

My corrections are minor; everything you wrote was grammatically correct.