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.
Have and have got (and have gotten) are used differently in British English and American English— in fact, it is one of the key distinctions between the two, though the American forms have reportedly become more common in the UK. Some examination is covered in What do "have", "get" and "got" mean? as well as What do you have to say for yourself? / What have you got to say for yourself? . Also see at EL&U, “have” vs.“have got” in American and British English and many others.
The Separated by a Common Language blog, by a University of Sussex linguist, offers a quick overview of do you have versus have you got for asking about possession. A search on corpora returned these frequencies:
AmE: Do you have = 3092, Have you got = 99. So 31:1.
BrE: Do you have = 245, Have you got = 450. So 1:<2.
In summary, she concludes
- If you are on a UK street corner, say Have you got a pineapple?
- If you are on a US street corner, say Do you have a pineapple?
- If you say Have you a pineapple?, you risk assault for non-normative behavio(u)r.
Separately, it's not clear what your example sentences mean. As noted in Do you have a / the time?, if you mean you are unaware of the time of day, you would say the time as another answer has indicated. It can also be used if referring to some known block of time, e.g. I don't have the time to discuss this at the moment. But the zero article can be appropriate if referring to time as an uncountable property, thus I don't have time to discuss this at the moment.
Best Answer
There are no real differences in meaning between any of them in a general sense, but they are not necessarily interchangeable. The right form/s to use can vary depending on the subject you insert.