OK, I'll give it a go.
I am not great on the electrical theory behind how a pickup works. I am not proud and more than happy for correction. I think I can answer your questions (or some of them) in a layman's fashion.
As I said, I am happy to be corrected by those who understand this stuff better than me.
In short, a pickup is a copper wire coil wrapped around magnets.
When a string moves in the magnetic field of the pickup, a current is induced in the coil.
A pickup works by producing an electrical signal that is transferred from the guitar to an amplifier and converted to sound by a speaker.
The signal is affected by the resistance of the coil. A so called "overwound" pickup has more wire wound on and all other things being equal (wire specifics, magnet characteristics) produces more signal than a pickup with less winds. The amount you can overwind depends on the amount of wire you can wind on.
The answers to your questions depend a little on the specific multimeter you have.
I have a Digitech DMM Autoranging.
To measure resistance of a pickup, I connect up as per the instruction with my unit. That is black probe lead to COM socket, red to VOhmmA. I set the rotary switch to Ohms and then select the desired range. Pickups are typically single digit or low double digit k Ohm resistance when working. Touch a probe to each end of the circuit being tested and note the display.
My TB plus pickups I just pulled out were about 9.7k Ohms.
You will notice a TBird pickup has a single lead. This is one of the Chinabuckers. The lead on a Gibson TB + is a little different but essentially the same.
As I understand it, the hot is inside the outer braiding, which is earth. The hot is exposed for the last little bit. Touch one probe to the end and the other to the outer casing of the lead and you should get a resistance reading, if you have done all the rest correctly and the pickup doesn't have a discontinuity (busted). In mine a discontinuity is indicated by a 0 reading or O/L, I can't remember.
Hope that helps and to be corrected/ educated.