You can keep a handgun in your car (as long as it is out of sight) even if you don't have a CHL as part of the castle doctrine....
however, I would hate to get into a pissing contest with a cop over that who may not know that law...
Everyone knows that law. If they truly hassle you about it, just say you're on your way to xyz in a different county... One more thing, if you have a tx chl but aren't carrying, you still have to inform the officer. If they run your license and find out about the chl that way, D:
The shooting test is easy unless you've never shot a gun before and definitely shouldn't possess one.