As always, if you are in doubt about what to do, the best advice anyone should give you is to call a licensed electrician to advise what work is needed.
Before you do any work yourself,
on electrical circuits, equipment or appliances,
always use a test meter to ensure the circuit is, in fact, de-energized.
IF YOU ARE NOT ALREADY SURE YOU CAN DO THIS JOB
SAFELY AND COMPETENTLY
REFER THIS WORK TO QUALIFIED PROFESSIONALS.
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Depends on the solder used. If silver solder is used it is actually stronger than the pipe itself.
Soldering iron, solder, flux
no
I think by 'cross wiring' you mean reverse polarity. This means the hot wire is connected to the neutral screw and the neutral wire is connected to the hot screw. This shouldn't have any impact on an AC motor, since AC voltage already changes polarity 60 times per second.
This is not possible. You must replace the diode.