1) See where it says "IF"?
Yes, you DO need a dedicated ground and separate neutral. A 14-50R is a 4-prong receptacles that requires four conductors. This is a "120/240v" circuit, NOT a "240v" circuit.
2) Yes, it would be wrong, but not non-compliant. Odd, I know. I would make sure the cord was indeed a 50A range cord.
3) If you use a 30A breaker you can use 10/3 w/ground cable. If you are going with the 50A use 6/3 w/g cable.