What forms of randomness are 'allowed' in FPRASs?
It's the standard model for any randomized algorithm, e.g., generate a random bit.

You can't generate a uniformly random number in the unit interval in the standard model.  You can't even represent a real number in a finite amount of space.  If you want to compute with real numbers, you need a different model of computation designed for reasoning about computation with real numbers.