Wheel squeaking at slow speeds and slight play in the wheel bearings, related?
If there is noticeable play in the wheel bearings, they are worn or need adjusting. Noise is most likely related to this.

The difference when rotating the wheel forward or back, or off the ground is due to the different loads on it.

You first need to figure out what kind of bearings you have in your hub. Cartridge bearing should just be replaced. Cup and cone style can be disassembled re-greased and adjusted (or replaced if they are worn out).