I'm not sure what you mean by "really loose" or "not turn as a unit". If you mean that you can turn one cog without turning the others, it sounds like something is seriously wrong.
Besides that, a 7 speed is possibly a freewheel, while a 9 or 10 speed would be a freehub. Sheldon Brown's pages for both are:
http://www.sheldonbrown.com/freewheels.html
http://www.sheldonbrown.com/k7.html
If you've got a wheel made for a freewheel, you can't go higher than 8 speeds, because they never made 9 or 10 speed freewheels.
If what you have is a freehub, then you can probably put a 9 or 10 speed cluster on it. The derailleur should work just fine either way, all Shimano derailleurs have the same pull ratios. It's the shifters that may be an issue. If you have indexed shifting, you can't use 9 speed shifters on a 7 speed cluster. At least, not without some extra work, like using a J-Tek ShiftMate. If you've got friction shifting, then it shouldn't be a problem at all.
Check out Sheldon's pages listed above, and you will probably find out all the answers you need.
Keith