Ungrounded and cloth jacket wiring

I have a 1941 house with plaster and lathe walls with ungrounded outlets and cloth jacket wiring at the outlets.

I don't believethe wiring is K&T as there is a mix of NM and BX wiring in the basement that goes to a breaker panel in the basement but with the exception of an addition, the outlets are wired to the cloth jacket wires.

I am looking to replace some worn out switches and outlets, which I've done plenty of times with the colored wires at the outlets, but I don't have any idea how to identify which wire is hot or neutral with the cloth jackets. I've tried just to put on new outlets doing a one to one swap but have had mixed luck.

Here are my questions:

1. How do I identify which wire is neutral or hot?
2. What is the best way to ground the outlets?
3. Will a single GFCI outlet on a circuit be enough to ground the circuit or does every outlet need to be GFCI?