correct form

<<I can speak today, or Sunday, or next week. I care a lot about my english so I'm keeping studing although I'm on vacation. >> , is this acceptable?

We can understand what you say but it's not proper English.  I suggest,

" I would like to speak in English today, Sunday or next week.  I care very much about this language.  So I will keep on studying even though I'm on vacation."

Correct Form.

<<I can speak today, Sunday, or next week. I care a lot about my English, so I'm continuing to study even though I'm on vacation. >>  Is this acceptable?

I understood you perfectly, so yes, it's acceptable.

Good luck with your studies.

Phil.