1. The voltage for the UK is 220/240 volts, yet for the US, it is 110?
can I use the first PC which HAS got a voltage selector switch by switching the voltage to 110 volts and using it that way over there?
Correct, but you may need to purchase a power lead with the American plug.
2. How can I go about using the 2nd PC in the US if it does not have a voltage selector switch?
You will need to change the PSU to one supporting 110V AC input.