No, a power cable from the PSU should not be at the back of the motherboard.
No, a power cable from the PSU should not be at the back of the motherboard.
As long as it isn't being squeezed and is properly linked, everything is okay. The way the cable is laid doesn't seem unusual.
I actually connected the EPS cable from the motherboard to the case, even in older builds without built-in management, and it worked perfectly because I avoided cutting into the insulation. You're definitely safe there!
Absolutely, it's definitely not a problem. In fact, I'd say it's quite common.