My P250 did the same thing. The cutting off part and not wanting to restart. The ignition switch was bad. The Fiat 124 Ignition switch is the same part. Buy one, it comes with a new key and tumbler asym. The only mod was a I had to make a jumper wire because in the start position it kills power to the circut for the run position, but activates 2 poles in the start position. A simple jumper cured the problem and has worked great.

Hope this helps.

Check your alignment for the steering problem and your lower control arm bushings.

Joe Frazar