I'd look at having the tires rebalanced first - alignment is more for tracking and tire positioning... so if the car isn't pulling to the right or left consistently, it's probably OK.
As for your electrical gremlins, they all sound like separate problems to me.
-A/C controllers are sometimes intermittant. I assume it still works, but just the display comes and goes? (You can have it rebuilt for $100 at
http://www.jerrytucker.net)
-Non Starting - the wiggling of the selector makes me think that the shift interlock switch needs to be replaced or adjusted. That is the switch that only lets you start the car when it's in "P" or "N" (Not sure on the parts price here - call Joe at
http://www.infinitipartsusa.com")
-Steering wheel - there are two slide potentiometers under the steering column (much like a slide volume control on a radio or TV) that tells the car where the wheel is. These get dirty and cause intermittant problems. Sometimes you can run the wheel up and down several times manually and make the problem disappear for a while because this wipes the dirt to one end of the switch... (I've had success cleaning them with electrical contact cleaner, but I think the pair of switches would be less than $20 to replace - Joe could tell you)
Sounds like you're on your way to getting the Q in good shape - good luck!
Heath