MIR, if you are trying to watch embedded youtube videos, they should open in the youtube app no problem. If they are Flash, you are out of luck. Flash is on the way out, and doesn't support mobile devices anymore. If they are HTML5, I have no idea why they aren't working. HTML5 is catching on, but a ton of sites still use Flash embedded. Try switching to the mobile version of the site, that might help.
Your connection issues are weird, as well as your apps force closing. If it continues to be a problem bring it up with Sprint. It might be as simple as a factory reset.
EDIT: I might add, I have the HTC One X (ATT version of the EVO LTE) running Jelly Bean and I can play most embedded videos no problem, so that's not a Jelly Bean problem.