Not sure the two problems are related, but could be.
I would first look at the steering column...turning the wheel could
be shorting a wire and there are wires in the column.
Your ignition sw module could be out of adjustment.
The key is on the column and a link goes from the lock cylinder
to the sw module on the bottom of the column. When in "run"
the contacts may be just barely making and a bump or that
bunch of keys on the keychain wiggle the switch and break the
connection.
An easy test would be to remove the ignition key from the
keyring ....eliminating any extra weight....drive the car and see if
the problem goes away