As for the walking around, our Lela has done that for the last 6,5 years. Her sister sits still while pooping. Personal thing, I guess. As for the watery-ness: we feed raw meat and this gives much better stool (and better coat and other things): thicker, and about 40% less, no more diarrhea which they had weekly when on kibble (even high quality). Maybe you could try it, and add probiotics for a while to build the intestinal flora. Cooked pumpkin and sweet potatoe are also great to end intestinal trouble (no rice and chicken).
I would say it is too early to leave him alone. There is so much he needs to learn and grow accustomed to at this age. Can you organize some daycare? It is easy for me to say, because I work at home and was with our pup all the time (I guess it was me who could not do without her....) Enjoy, they grow up so fast.
What may help is:
- don't tower over the dog and stand right in front of him or look him in the eye directly; sit on your hunches beside him, facing the same direction and be calm;
- offer the collar and a treat just in front of it, so he has an incentive to put his head forward into the collar.