Is my puppy abnormally smart?

Unusually loyal? probably! But I don't think unusually "smart" per se.
 
One of my Jack Russell puppies did this. Never really left my sight, even off lead, never was any trouble to control off lead. She did go through a phase where she was testing limits, but for the most part she'd zig-zag along behind me.
 
I think some puppies are a) more dependent than others or b) consider you to be WAY more interesting than anything else going on!
 
PRAISE THAT BEHAVIOR!!! If you work it now, you'll have a lot less problems later teaching heel. I'd suggest you use it to your advantage and train a command for following you around... it would be a great way to capitalize on your little one's loyalty []
 

No!!!!  He isn't exceptionally smart (well, he could be, but this would not be why).
Small pups tend to follow easily.  This is a great time to start teaching him to walk nicely by your side and attach a cue, like "let's go" and reward him as he stays there. 
All pups, however, go through a stage where they begin to explore the world on their own, and even if you have trained him, he may ignore your commands and go off anyway.  The age at which this happens is not the same with all dogs. 
Please, for his safety, keep him leashed when he is outside of a safe fenced area.  A dog this small is an easy target, and it is not unheard of for them to be snatched up by coyotes or birds of prey yards from where their owners are standing.  Heck, I remember someone lost a 3 month old Aussie pup to a coyote, and the dog was leashed.

this is normal for a young pup, they stick close. As he matures he'll start going further and further away. It's great you're starting off-leash work at this age. If you continue to practice and reward him for keeping an eye on you, staying close, and coming when called he'll mature into a lovely companion. Just watch out for when he starts his "independent:" phase. You'll probably need to put him on a long line for a few months for his own safety.

Good to know.

Also what kinds of treats do you recommend if he is a BARF diet dog? I want something he will love some much that is really special but is healthy for him at the same time.

you can buy all sorts of freeze-dried meats that make good healthy treats for such dogs-- possibly not in your local pet store though. Look at websites: a place for paws, sitstay.com, clean run all have good selections of meat treats. I don't like to handle raw meat myself, so I cook meat for treats. Cubes of chicken and beef, things like that.