1. No. If you tell the UA GA at GSO they wil check it to PRG. Just have your LH flight info available.
2. It depends on who ground handles LH at PRG. I believe LH agents will do it. At smaller stations the agents tend to be contracted and thus some may not be faimilar with LH computer systems. But Amadeus is much more widely used than Apollo.
3. Just book it separtely with plenty of connection times in each stop.