#1
Alright for a song I'm learning a few of the bars are a C chord with strum pattern DDUUDU. I'm wondering if i can just bring my thumb and not push down on the low E, but just mute it by holding my thumb to it.
#2
Yeah, you could do that. It's how blues guitarists play some chords.

Careful though, if it hurts, you're doing it wrong, so stop.
Current gear:
Carvin CT6M
TC Electronics Dark Matter distortion
Harley Benton 2x12, with Celestion V30s
Laney Ironheart 60w tube amp
#3
Sure muting with the "thumb over" technique is fine really, and a great thing to learn.