I think this is a Phantom 1, but on the bottom it says "P330"

I think that is the V1.1.1 of the Phantom?

The wire that is cut, that is just for a gimbal?

It has aftermarket props on it, is there DJI self tightning props for this version, like on the Phantom 2?

The 1.1.1 came with self tightening props.  

My 1.1.1 says MODEL P330D   (the letter "D" after P330)

Looks like a older P1.

Only way you can get the self tightening props on is to replace the motors. The wire is for a gimbal as you thought.

I thought the very first version had the kind of props that you had to tighten a nut above the prop.  That must be a museum piece -- it looks like it just came out of the box.

Yeah that is a old one.