Fabulous work, thank you so much for posting the photos!
I'm thinking some of the beads are what some companies call glass "globs" or "nuggets". They can be ordered by the pound from any stained glass company. They are freeform, in different sizes and colors, flat on one side and rounded on the other. Loads of fun.
The glue is probably an epoxy, but for outdoor use I like clear silicone.
The backing could be most anything, including glass or plexi. I'd use plexi in an outdoor setting, because it's much less breakable.