Actually, while here below we are discussing “those”, you were above asking about “these”. Does that make sense?
Either way the examples do have broadly similar meanings but there are significant differences, including these below:
I finished my homework.
I completed my homework at some time in the past. I might have started the work previously and set it aside, but during the session in question, I completed the work.
I am finished with my homework.
I completed whatever homework I had and I do not expect any more; not in the immediate future and not impossibly, never.
I have finished my homework.
I have just now completed my homework, seconds or at most minutes ago.
I did my homework.
Very much the same as “I finished my homework.”
Some might say "did" could as easily mean "finished" or simply "worked on".
Some might say “finished” could indicate a session resumed and “did”, completion in a single session.
I am done with my homework.
Not just similar; probably identical to “I am finished with my homework.
I have done my homework.
Very much the same as “I have finished my homework” but rather less immediate. “Done” is more likely than “finished” to imply “I did it yesterday”.
Further, “I am done / finished with my (anything)” are anchored within the same range of meaning only by that possessive “my”.
With the possessive “my” the sentence is a specific, factual report about the fate of a concrete and measurable thing.
Without the possessive “my” it would become instead a generic philosophical statement of intent about an abstract and unmeasurable subject.