Does fuse amperage required change with voltage

No, it's R that's inverse. If R goes up, less current is drawn at any given voltage. And the power formula is not inverse. You must have a formula where one value is the divisor /below the fraction line to make it inverse.

Current cannot be "changed" except by the EFFECT of changing the voltage or resistance.

Obviously, you cannot manually change the resistance of something such as a light bulb. But an example is the dash dimmer control on your headlight switch. That is nothing more than a variable resistance. To make the lamps brighter, you are manually DEcreasing the resistance of the dimmer control.

This increases voltage TO the lamps

and CAUSES current to increase.

With wattage, in which resistance is a constant, like a baseboard heater, and voltage is known and can be changed, current can be affected in that way.

If you could "lash up" a tapped transformer (or use what is called an autotransformer, or Variac) you can manually change the voltage delivered to the load, in this case a heater.

As you increase voltage, R stays about the same, and current must increase. With a constant R, ohms law tells us that current will be a simple relationship to voltage, IE if we double voltage, current will double.

This means wattage (power) will NOT double with a 2x voltage increase, it will increase by FOUR

I=E/R

If E is 110V, and R is 55 ohms, I will be 2A

If E is 220V, R stays the same, I will be 4 A

So our power will be

P=IE

P=110V x 2A or 220 watts
P=220V x 4A or 880 watts.