can Worgen ride mounts in WoW?

Answer 1

Yes, you can. But your reputation lvl need to be  exalted, with this reputation lvl you can purchase and train to ride mounts of another race. If you are a warclock at lvl 20 you can learn the summon felsteed spell.

Answer 2

Absolutely.  You can use any mount that you have obtained on a Worgen character.  The difference for Worgens is that they don't actually have their own racial mount, every Worgen at level 20 learns "Running Wild" which allows them to run at mount speed on all fours.

All normal mounts follow their normal restrictions.