I was a vegetarian for several years and still live in a vegetarian household, thus all of my cooking experience is with vegetarian food. My partner and I have made an arrangement that I can cook meat for myself on our gas barbecue. Since I have no experience with cooking meat, I'd like to learn as many techniques as I can. Are barbecues only good for grilling or are their other techniques I can try such as pot roasts, tagines etc?
First off, you can use a gas grill as a gas burner, and cook anything you could on the stove. It won't be very efficient, and won't be as pleasant as using a stove, but it'll work. The one big inconvenience is that since the burner won't be appropriately sized to the pan, or directly beneath it, you'll need pots and pans that can handle heat all around - in particular, you can't use anything that can't take the heat on the handle. Cast iron might be your best bet. But from there you can do whatever you want - saute, sear, etc. You're not really limited to one technique.
You can also essentially use the grill as an oven if you want to. You won't have precise temperature control like you would in the oven, and the temperature will vary more from side to side and top to bottom than it would in an oven, but it can reach the same kinds of temperatures. If you get a thermometer with a probe that can be left inside the grill, then you'll be able to adjust the heat as needed and get a sufficiently precise temperature to do most things you could do in the oven.
You'll want to use indirect heat to do this, so that whatever you're cooking isn't incredibly hot on the bottom. If you have three burners, you can use the two on the sides and put the food in the middle; if you have two you'll have to use one on one side and put the food on the other, resulting in somewhat less even heating.
Here again, you're not really limited to one technique. You can do braised things inside a dutch oven (like a pot roast). You can wrap things up in foil and roast them. You'll have a bit more trouble with things that are meant to cook open and care more about even heating, so for example thinner slices of meat (or fish filets) on a baking sheet might not be a great idea, but there's still plenty you can do.
All-in-all, I wouldn't think of this as learning a list of techniques. I'd just look for recipes you're interested in trying, and see if they seem like they'll work on the grill given all that.
You may be able to use the gas grill for "low & slow" BBQ, although it wouldn't be ideal. You'd need someplace to put the wood chips to make the smoke, and I assume, as does your grill manufacturer, that the grill is located in a well-ventilated area. The grill would need to be set low, and you would absolutely have to make sure that you had a good-sized grease catcher in place.
You could try a pork loin, for example, on the end of the grill away from your burner(s) (e.g., don't run all 3 or all 4 burners, but only the ones away from your meat). You'll want a meat thermometer and aim for an internal temp of 165 degrees Farenheit.
Prior to cooking, marinate it in apple cider overnight, coat with a sugar/salt-based dry rub (no affiliation with the linked site; the rub is similar to the one I make myself, although I don't use the cumin nor the thyme), and give it a try. It's certainly not a traditional tool for smoking, but it's not that different, and people have good success with gas-powered smokers and even electric ones, although the taste is less intense than a true wood-fired smoker.
The real problem in this scenario is that you'll have an entire pork loin all to yourself ;-) For that, don't forget that any number of vegetables also taste great grilled, or even smoked. :-)