How can I prevent my screen from turning off while on a phone call?
Keep screen on during calls

That setting is not available on all phones, but if it was it would be under:
Home > Settings > Call Settings > [Display >] ...

But as for the difficulty turning the screen on

Be sure that the power button does not end calls (Settings > Accessibility > Power Button ends call : make sure it is UNchecked)

Then just pull the phone away and press the power button to turn the screen on.