Aside from the slight variations already pointed out, the simple answer is that there is a massive supply of power in the grid and pulling a few extra amps normally does not burden the system.
Yes they do. They supply whatever current the load needs up to the limit of the circuit breaker. The voltage does, in reality, sag slightly due to wire drop, But; not very much.
Theoretically, yes they do. Practically, no. If load resistance decreases, V out decreases some, if load resistance increases, V out increases some. All wires have a resistance, even the wires from a supply point to an electrical outlet.
Not an absolutely true statement. Even if the Voltage that feeds a house is well regulated at the input to the line that feeds the house there is still a Voltage drop across the resistance of the feeder line that varies with total house load current. Of course this Voltage drop subtracts from the no load Voltage present at the outlets. This is normally not a problem because most all home electrical equipment is designed to operate properly over the range of Voltage variations caused by normal load variations.
