1) What exactly are side stitches when you run? 2) What is the cause of them?
There isn't really any way to accurately identify exactly what a side stitch is, however, it can be caused by the pressure from the pumping of your legs pressing up on your diaphragm and the pressure from your rapid breathing in your lungs pressing down on your diaphragm. This causes uncomfortable pain in your abdomen because the pressure is squeezing your frame tighter and therefore cutting off blood and oxygen flow.
Also, eating right before a run can cause side stitches too.
3) Are certain people more likely to get them than others?
Yes, those who have improper breathing technique, poor posture, or a weak core. These people are more susceptible. I coach about this a lot during my runs, and I encourage my trainees to take huge deep "belly breathing" breathes even when you don't feel like you need to, every 3 minutes or so in a run. The more oxygen you can get to your body, the more efficiently you will run. Those who have shallow chest breathing are more likely to be affected by side stitches.
4) If you're prone to them, can you do anything to minimize them?
Core exercises, practice proper breathing technique and improve V02 max (lung capacity) through speed work and hill repeats. (i.e. do hill repeats, speed work, and metabolic conditioning with strength movements that incorporate your core and hip extension.)
5) Are there certain exercises you can do to minimize their frequency or pain?
Doing a few core exercises before your run can help with this- and like I said before, improving overall lung capacity through speed work and hill repeats will also help.
6) Does food play a role in causing side stitches/ab cramps?
Yes, running on a full stomach will not be pleasant. All the pressure in your diaphragm from the pounding in your legs and rapid breathing in your lungs will smash your stomach and inevitably cause cramps from the body's lack of oxygen/blood flow.
7) What do you recommend for battling side stitches mid-run or race?
Stop. And every 10 seconds take a huge deep breath (DEEP belly breathing). Fill lungs up to full capacity and exhale. Do this for 60 seconds and progress back into race pace, starting at a light jog