"I make breakfast" is unnatural for any English speaker in the present tense and not grammatically correct. It would be correctly said "I am making/preparing/cooking breakfast".
I am preparing a breakfast, why not?
I don't think you need "a" here, but "I'm preparing breakfast" should definitely be accepted.
"A", "the" and no article are all accepted here. The problem was that the word "prepare" wasn't on the list. Fixed it, thanks!