Welcome back to the forum. However, I am concerned that you are spending too much time and emotional energy worrying about minor health problems. This is your third question on this forum. Nobody wants genital warts or other HPV infections, but being infected is not abnormal and rarely leads to serious health outcomes, as long as certain precautions are taken, such as regular pap smears in women.
To your questions:
1) Direct examination by a dermatologist is far more accurate than any guess I can make about the nature of this problem. If s/he isn't concerned, neither am I -- and neither should you be worried about it.
2) Although HPV DNA can persist indefinitely (the experts debate how often this is the case), most HPV infections clear up to a point they cannot be detected by biopsy or any other method. Biopsy is never done to diagnose HPV in people without abnormal pap smears, warts, of other visible lesions.
3) It is doubtful the lesions on your fingers and palms are warts. Multiple hand warts are rare in adults and would always clear up on their own in a few months. If you are concerned about this, show them to your dermatologist then follow his or her advice about it. However, in the off chance you actually have hand warts, you can be confident they are caused by one of the non-genital HPV types that would be unlikely to be sexually transmitted.
4) Some doctors probably don't understand warts and HPV, and others may simply use the terms loosely without carefully thinking about it.
5) I'm not sure I understand this question. There is no hard and fast interval for HPV clearance and inability to transmit to partners; the more time passes without recurrence, the more likely the infection is gone and will not be transmitted to partners. At this point (6+ months) it is likely you are home free.
I'll close by reemphasizing my opening comments. Please read this thread, which gives an overall perspective on genital HPV infections. You should find the information reassuring:
http://www.medhelp.org/posts/STDs/HPV-Transmission/show/1522088
Best regards-- HHH, MD