2013Civic

I'm still trying to troubleshoot my 2013 Civic that gives off a metal taste in the mouth and head tightness/"duh" feeling only when driving (but not merely sitting in the car while not running--it's not the fabric). No exhaust leak can be detected visually and it passes emissions.

So now I turn to other possible solutions:

1) Which dashboard indicator lights should light up when turning the key in the ignition far enough to turn on the battery but not far enough to actually start the car? Are there any that would stay off no matter what (I see that my "H" for heat that is next to the "C" symbol for coolant temp, for instance, never lights up when turning the key--is that normal?)? I want to make sure that all of my dash indicator lights are working properly.

2) Which indicator light should light up on the dash when there is an O2 or catalytic converter problem? Are there situations where those two parts would go bad and not show on the dash lights as being a problem?

3) Would a bad head gasket issue show up typically in a warning light on the dashboard?

4) Should it turn out that for some reason certain dashboard indicator lights have never worked since I drove the car off the lot, and there is a mechanical problem that should have set off an indicator light, would a code reader be able to tell me the history of the mechanical problem (specific problem + when it began) even though the dash light isn't lit?

And for bonus points:

5) How easy is it to test a catalytic converter? Can a non-Honda mechanic do it?

6) How easy is it to test whether the dashboard indicator lights are linked to the engine properly? Is that something a non-Honda mechanic could do easily?

7) Is the Japanese radiation rumor a real threat? Worth a Geiger counter test? Grasping at straws here; it's just really unsafe to drive. A 25-minute jaunt in rush hour stop-and-go recently landed my husband in the ER with nausea/vomit response, a neurological tics, extreme dizziness, face flushing, high blood pressure, and feeling mentally "slow" and tired. Blood gas tests several hours after exiting car indicate not a CO problem, and he is in perfect health outside of what the car caused.

8) What would cause a 134a leak to come into the cabin? Could a bad head gasket? A bad AC system? How can you test for a 134a leak? Again, is this something a non-Honda tech could do easily?

Thanks in advance for your replies. Hopefully something can be figured out. I am truly stumped, and all Honda seems to do is drive it around with the windows rolled down for a few miles and tell me nothing's wrong. I asked why mechanical diagnostic tests of any kind have been avoided, and no one can give me a good answer. Obviously, driving it around the block is not the diagnostic tool needed. I've struck out three times with Honda Service at this point, so I'm going to have to branch out to others who can help me find out what's going on with this car.

Any advice is appreciated! Thanks!