Yes. And AC voltage, also.
No. It increases the amplitude of the AC voltage.
The impedances are fixed. The output voltage is proportional to the input voltage, just larger. The power amplifier makes the AC voltage even bigger and that AC drives the speakers.
The guitar gets whatever ground from the input jack on the amplifier. This is a zero volt reference that the input signal is measured against, but it doesn't have to actually be a connection to Earth. The main value of having the amplifier actually connected to Earth is that this means there is no difference in voltage between the cases of the pickups (that act as shields around the coils) and Earth. This helps reduce hum pickup because there is less capacitive current traveling up and down the guitar cable shield. But having a good ground connection also means that you will feel a shock if you are touching the metal on the guitar and also touch something else that has voltage with respect to Earth on it. So many tube amplifiers have a floating guitar common (outside barrel of the cable plug).