I think both of your suggestions sound a little off. I'd suggest
Not likely=
(1) I probably haven't finished my homework.
(2) I don't think so. (with a heavy emphasis on think – to indicate sarcasm, as mentioned in The Photon's answer)
However, I must ask: Did this question come straight from a test? Or did you make it up, or alter it somehow?
It seems unlikely that the phrase "not likely" would be used in the first person, not if we are talking about something that isn't in the future. The word "likely" is used to express a high probability. Therefore, if you ask me whether or not I've finished my homework, either I have finished it, or I haven't – there's no "likely" involved, because there's no uncertainty involved.
I could see the phrase not likely being used in this context (future tense):
Do you think you'll have your homework finished by 10 o'clock?
Not likely. (Meaning: "I probably won't.")
or this context (third person):
Do you think Ariana has finished her homework?
Not likely. (Meaning: "I doubt that she has.")
However, it's very hard to imagine me using "Not likely" as an answer to the question, "Have you finished your homework?" Then again, perhaps that's the point of the question; if it's meant to be an incorrect answer, maybe it's not supposed to sound interpretable.
In many contexts, the meanings are pretty much the same, but you might hear finished more often than completed in casual conversation. For example:
I've finished my shopping.
She finished the song.
He finished the race.
I could use completed in those sentences – the meaning wouldn't change, but the register might sound off.
The word completed can convey some sense of accomplishment. In the context of a race, it might work when the race is a major achievement:
He completed his first marathon last year.
Homework, though, is not really a major achievement, so I think you'd hear finished more often in casual conversation:
“Joey, where are you going? Did you finish your homework?”
That said, you might see completed in more formal contexts, such as a paper on education, or a course syllabus:
Students must complete six homework assignments during the semester.
Best Answer
"I started watching TV after I had finished my homework." In this case, you want to use the past participle. It is also common to hear "I started watching TV after I finished my homework." Those are really the only correct ones. Because you are saying that you started watching TV, you wouldn't be able to say "have finished."
If you are talking about your general routine, it would be okay to say, "I start watching TV after I have finished my homework" or "after I finish my homework."