“1) Does pavutti kamma bhava mean one will get the vipaka only within this current bhava we are in right now? Or does it also involve vipaka in future bhava that will come after this current bhava?”
They could occur in this bhava or future bhava.
“2) Does uppatthi kamma bhava mean a vipaka that is an entirely brand new bhava/existence?”
Yes. That is a new bhava, not a jati within a bhava. For example, when one is in the human bhava, one may be born (jati) many times with a physical human body, and in between those, one lives with just the mental body (gandhabba).
Cuti-patisandhi (or grasping a new bhava) happens only when the kammic energy for the current bhava is totally exhausted. When that happens the above human may grasp a new bhava of a deva, brahma, animal, etc.