Let's say that one branch of a fig has better looking leaves or slightly better fruit. Could this be a mutation? If so could I take a cutting from that branch and it keep those characistics that I like in the mother plant. Kind of like selective breeding. Like a modern day Mendel but with cuttings. Like the panache that doesnt get stripes.

I don't know much about this, but as I understand it, if it is a true genetic mutation and not just an extra vigorous branch or caused by some other non-genetic factor, then yes, cuttings or air layers should retain the same trait as the original branch.

What you're talking about is called a "sport" thats what its called when a single branch happens to have different characteristics. Definitely a good idea to isolate that branch and preserve the different strain.

So my black mission has fmv but not too bad and one branch doesnt show it on the leaves. I know it's in there but cuttings from that brach might not show it. Could it be possible after a few "generations?" not show it at all and maybe have clean tree. I know it's in the DNA but i am hoping it may lie dormant permanently