You can run a wire from one of the outdoor outlets. 110, 115, and 120 volt circuits are pretty much interchangeable. An appliance rated for one of these will work fine on any of them. You may need to check the pump's amperage to be sure it isn't greater than the capacity of the circuit breaker.
You need to check the NEC concerning pool pumps. The pump must be GFCI protected. A licensed electrician should be consulted to ensure this pool system is done correctly and for the safety of people using the pool.
Yes, no problem with a small change of voltage.
You should have no problem as long as the pug fits into the outlet. Common house hold voltages range up to 120V.
Yes you can safely do this. Most appliances that are marked 115 volts will operate on outlet between 110 and 120 volts safely.
In the US, standard household receptacles are 120V, but historically they used to be called 110V. So the two are the same thing - at least in the US. Depending on the age of the electrical device the nameplate may say: 110v 115v 117v 120v and they all are referring to a standard household receptacle.
I've had a 115V Frigidaire window unit plugged into my standard 110V wall socket for a few years. Works great!
Yes
Yes, all wall receptacles are rated at 125 or 130 volts.
Yes, no problem at all.
US outlet and US air conditioner = Yes
Yes. It's functionally the same.
Volt....common household outlets are 115V
No, the circuit should not be energized when checking the resistance of a circuit.