Question

The relationship between pressure and volume, when moles and temperature of a gas are held constant, is: PV = k. We could say then, that:
If the volume of the gas is doubled, the pressure also doubles.
If the volume of a gas is halved, the pressure is doubled.
If the volume of gas is doubled, the pressure is unaffected.
If the volume of a gas is halved, the pressure is tripled.

Answer 1

You can say that if the volume of the gas is halved, the pressure is doubled.

The expression shows that pressure and volume are inversely proportional if temperature and amount of gas is held constant.  This means that if volume goes down the pressure needs to go up.  That also means that in order to maintain the K value, if pressure is doubled the volume needs to be halved and if the pressure is halved the volume needs to be doubled.

This relationship only works if we assume everything else (Temperature and moles of gas) to be constant.