It is unlikely the possum will let you, but even if it does, the answer is "no". The possum could easily bite you, and they are known harbourers of both fleas and ticks.
Yes. But not straight away - Only when they get used to you hand feeding them for a while and build so much trust that when they come visit you they don't get scared at any random time and for this...
Relating to brush possums:
Possums can become a pest, going through rubbish bins, damaging fruit trees and eating other produce.
If relocated, they can return from around 10km away from their home....