To prevent any potential litigious claim, exception or biases by any litigious persons. Yes as far as I am aware this is a common policy of most retail establishments.

Not sure what kind of business that is, but it is not uncommon for employees not to serve family, perhaps even friends. It's simply meant to eliminate any suspicion of free extras or improprieties. Cashiers would certainly not check out a family member or friend if at all possible. I know of no law that would contradict. It's usually at stores discretion.

pretty typical of all places of employment

That's an insane and stupid rule. However, it is likely within the rights of your boss to do so. Doesn't make it any less wrong though.

65 is legal working age?

catch 22 on this. Some places have rules about serving family members