I have recently acquired a very nice m1 carbine. I don't know much about these but was curious about some things I have noticed. With the gun fully assembled the whole trigger assembly can very slightly move around, is that normal? the whole receiver can wiggle and move around in the stock, is that normal? My m1 garand fits together in the stock tight as a tick, this thing is almost loose in the stock. Won't that effect accuracy? Is there anything I can do about it? Is it normal?

Doesn't sound good for accuracy.

IIRC the barrel should be drawn down a bit with the barrel band.  The hook on the rear of the receiver should be square in the metal block that is screwed behind it to the stock.  

I would also check the fit and pins of the trigger assembly.  Maybe someone made up one for a missing pin?  

I lucked out with m1 carbines in the past, they were well fitted.

Trigger housing movement is normal.  Receiver movement is not.  The fit of the barreled receiver to the stock/recoil plate should be tight enough that you have to pull down slightly on the barrel to get the barrel band seated during reassembly, and the barreled receiver should not have any excess movement in the stock once the carbine is totally reassembled.

The first thing I'd do would be to check to make sure that the screw on the recoil plate is snug.  (That is the T-shaped metal object embedded in the top of the stock behind the receiver.)  Also, check the screw on the barrel band as well.

If those are fine, then it may be a stock fit issue.

When the barrel band isn't on, the barrel lays flat in the stock there is no lift. Sounds like I found the problem. I guess I will disassemble and try and fix it. I will update tonight.

*Update* followed a guide I found elsewhere. It was just a process of mortaring the gun then tightening the screw, mortar, still loose?, tighten, mortar, still loose?, tighten. Now the receiver has zero movement. Mortaring doesn't make it loose either. Can still easily disassemble and about 1in barrel rise off the stock when reassembling.