umm...

I must do my homework now, but i will draw a fan art.
Because the deadline is approaching me!

I`m drawing this picture now (at the moment).

英語の勉強頑張ってください！

umm...

i must do my homework now but i will draw fan art.
I should be doing my homework but instead I am drawing fan art.

Because the deadline is approaching me!  What deadline are you referring to? your homework?

*Never start a sentence with the word "because," because "because" is a conjunction: meant to link two clauses/ideas together.

this picture is drawing now.
I'll assume the picture is the one you drew, so you would say "This is the picture that I drew."

or if its still a work in progress you can say something like " I drew this picture but its still a work in progress."