Ellie, I'd say you are smitten! He is such a stunning boy (I think I said that already). I too was thinking Papillon when you described him. I can answer a few things for you:

Always take a bag of yummy treats with you on vet visits, let the vet and techs give some when they finish with him. Bits of cheese or bits of hot dog, small of course, so they can give 2 or 3 each.

When dogs move to a new home, they go in to a sort of shock for 2 to 3 weeks before they settle in. So this is why you are seeing that initially he had to keep you in sight but with time he is OK to be in a different room from you. Quite normal. My newbie Tony followed me to the bathroom at my 3 AM trip for 3 weeks before he decided it was OK to remain comfy in bed.

Once he knows where that dead mouse is, he will go back there over and over until it is removed. Unlike we HuMoms who work to FORGET where the darn this is! Oh wait you already knew this, ha haaa.