To answer your first question: yes, the off-hand you’re after has a chance to drop in the chest you loot at the end of the dungeon. As far as I know, anything in the dungeon journal (for your specialization, of course,) has a chance to drop from mythic+ chests.
For your second question: I hope I’m understanding this properly but with raiding there are four different difficulties. LFR, Normal, Heroic, and Mythic. Mythic is the hardest of the four. For anything outside of LFR you will have to go to the group finder and either make your own group or join another person’s group.
Truthfully, if I were you then I think I would work on farming mythic+ for my off-hand. It seems like it would be a lot easier than doing Mythic EP with pugs (assuming you don’t have a guild that runs it, at least.)
I hope this helped, let me know if you have any more questions and I’ll do my best to help you out. 