This is not as easy as it looks, but I'll try to answer your Floyd question first:
Bryant was referring to the Floyd Rose
tremolo system.

It's basically a fancy tremolo bridge (you know, they have this whammy bar that you use for applying tremolo). It sits balanced on two studs in the guitar, has locking mechanisms for the strings etc.
The neck is a much more complicated issue. You will need to know what type of neck was on the guitar previously, so I recommend you try to find out what guitar this is. You see, if this guitar used to have a 22-fret neck, you will need to get one of those - or if it had a 24-fret neck, get one of those. This is important, because if you put the wrong type of neck on the guitar, you end up with a scale length that is off and the guitar would be impossible to get to intonate properly. I would guess from the pickup spacing in the picture that this guitar used to have a 22-fret neck, but I can't say for sure.
Secondly, the neck must have space for a locking nut. Since the guitar was built for a Floyd system, you will need the locking nut to keep it in tune while doing whammy bar acrobatics. An ordinary nut will work as long as you keep off the whammy bar though, but the guitar won't be "complete" without the locking nut.
Thirdly, having a neck that fits well with the neck pocket in the guitar body is instrumental for getting a nice sound. The more snug fit it is, the better. This is maybe the most problematic part of finding a good replacement neck.
Finally, I need to ask - what type of wood is the guitar body built from? If it's just a chunk of plywood, it will hardly be worth the effort or the costs.
'bane