Is it allowed to solder a cut wire back onto a motor. I havent modified the motor in any way, so is it still allowed?
It is legal as long as you don’t change the length of the wire.
It is both legal and common to repair damaged connectors. R15 a ii is the relevant rule:
A less expensive alternative (best if you have lots of wires to repair) is to crimp new pins onto the wire and insert a new housing: https://www.robosource.net/39-wire-repair