1) Not normal.
2) Not sure if what you're hearing is 'backlash.' Sounds like a bad ujoint or something to me. If it is gear backlash, whatever gearbox is doing it will have to be torn down and diagnosed.
3) Most likely.
If your diffs have excessive backlash, you will need to pull cover, use a dial indicator to measure, and compare with specs. Sounds more like a ujoint or something loose to me, check mounts, crossmembers, etc. You can even remove one drive shaft at a time and then re-test the vehicle and try to duplicate the noise.