I don't know diddley about 3-gun. I know it looks like fun. So, some basic questions:
Are the 3 guns interchangable during all stages? Can I choose to use a shotgun instead of my pistol?
**No, not at most matches. Generally targets are designated per weapon.
Run & Gun format?
Sometimes. There are many different types of stages at the different 3 gun matches. Heck there is even 4 (at least) different scoring systems.
How are points awarded? Total shots vs. total time?
Depends on if you are at a USPSA 3 gun, IPSC 3 gun, IMG, or under IronMan rules.
USPSA = your points/time for a hit factor - high factor wins the stage and get the max value, all others are divided by that factor for their percentage of the equivalent points
USPSA = also has a time + scoring system, your raw time + any penalties
IMG = pretty much a time plus system that generally means two hits on a target or one A and it is neutralized.
IronMan= time +/-, you can get bonuses under this system that reduce your overall time.
Some matches factor all the stages to a value of 100 points. Fastest time gets the 100 points on the stage.
Are you a shooter full-time? How'd you transition your hobby to your profession?
Sorry for the slow response, went to sleep. Now just catching up with the thread again.