Present perfect - one question + one extra

"I have already done my all homework today."

Can I use the present perfect tense with an adverbial of time "today"?

When I am talking about more tasks that I have been assigned by my teacher to complete, can I say "all homework"? Or how would you put stress on the fact that you have more than one task to complete (for example, to fill in papers in various subjects at home). In the Czech language we use the word "homework" as countable, that is not the case in English and that is why I am asking.

Thanks a lot in advance.