>Because I need to learn correct English, <something-- This part confuses me!>
Because I, too, need to learn correct and standard English, I wish we can learn language from each other.
>Not only grammatically correct <English>, but also natural-sounding English.
I want to learn not "English that is barely enough to communicate," but correct English. Not just grammatically correct, I want to write natural English.
(My comment: you know, we often understand what people mean even if there are grammar mistakes and awkward usages. But he doesn't want to be satisfied by only "being able to make him understood." )
>I can correct <something about English and Japanese>.
I can correct (your) English composition written in Japanese.
(I guess he means "Japanese composition. " Not English! lol)
All the rest looks good:)