#1
My Picking hand wrist has been hurting lately on the thumb side when I Roll my Wrist.

This pain does not happen when I play guitar, but Hurts my Wrist when I lift Objects.

Can playing guitar Improperly cause pains that would not appear during playing?

I may have just Sprained/Strained my wrist In a completely unrelated matter than guitar, But Im just wondering.
#2
Probably, but that's really a matter for a doctor. I recommend you get medical advice from a doctor, not random people on teh interwebz.

On the guitar side, it's always a good opportunity to make sure you're not doing anything that'll hurt you in the long run. Warm up properly, minimize the bend in your wrist when you play, don't use too much force, etc.