Hello lm, thank you, I'll try my best to answer your questions
I think you are right that there are definite similarities between fana/ nirvana/ moksha. Perhaps it is the same experience, after all, one cannot speak definately about these topics until one experiences them for oneself. To be honest, I am uncertain about the exact meaning of fana. From what I understand one could either think of fana as a mystical experience, seemingly random and life-changing. Or it is a definite stage upon the Way to enlightenment, a station of being and far more than just a passing experience, it is a way of living. Perhaps, even, that there is no difference between the two different meanings I have stated above and it is only a matter of being in such a state to know what that means.
There is, however, I believe, some difference in opinion (at least to those of us on the outside) about where fana is on the ladder towards god. For some sufis such as Hallaj, fana is the absolute end of the journey because one reaches home once one becomes united with the all, with god. For other sufis such as Ibn Arabi (and our very own The Tailor, I believe) there is a stage after fana called baka, which is the return to the world from god as a true individual.
As an analogy, one can think of the entire world as an ocean. We, as individuals, are just droplets in the ocean who are trying, ridiculously, to retain our egoistic little droplet as individuals and forgetting that we are all the same substance and all one ocean. Fana would then be the droplet realising that it is just a droplet in an ocean and merging with the greater whole. This would be the end of the story for Hallaj, however, Ibn Arabi would say that this is just going halfway. The rest of the journey is to become crystallised as the perfect image of god on earth, to become a pearl fashioned by the ocean itself. I think Allama Iqbal was in disagreement over this very point with Rumi where he felt that Rumi only wanted us to live as droplets in an ocean and not to become pearls, the absolute image of beauty on earth. I don't know if Rumi did actually believe what Allama Iqbal accuses him of but it fits in well with the analogy above.
I do think there is a similarity here between the ideas of fana and then baka with nirvana and then becoming a bhoddisatva. There is the same idea that nirvana is not the end of one's journey, but one has to return to the earth as the perfect individual, capable of leading others through example. I don't know exactly how buddhism ranks the two stations of being a buddha and being a bhoddisatva so cannot take this analogy further but there are some interesting parallels none the least.
I don't know if one can say that sufi concepts evolved out of hindu concepts. The mystical idea seems to me to be perennial, to be the inner meaning of every expression of human truth and so cannot really be said to have "originated" in a historical manner. The ladder to god, as the mystics understand it, is ahistorical, I believe and there is no specific beginning anywhere. To do so would be to make the same mistake as the catholic church as opposed to the gnostics of early christianity whereby god enters the world at a specific time and place and dogma is established, but as the gnostics understand it, the son of god enters into everybody and there is no dogma to follow.
Of course, this is all from my perspective standing outside of these traditions. I don't know if what I have said would be acceptable to those inside.