Regarding grilled food and gluten: There are two possibilities for getting gluten in grilled food, other than the usual ones. First, some charcoal briquettes are made with wheat as a binder. I switched to solid wood charcoal to avoid wheat and other peculiar things that can go into briquettes. The brand I use is from Whole Foods; it’s cheaper than the charcoal I find elsewhere.
Second, if the grill has been used to cook non-GF food, such as buns, you could suffer from cross-contamination. You can buy a replacement grill, which is fairly inexpensive for most grills. Or, you can use a pre-made aluminum liner; I can’t think what they’re called. Or, you can just put a piece of aluminum foil over the grill and cut slits through it.
Watch out for barbeque sauces. They very often contain gluten. It may be in the form of teriyaki sauce.