Risks in climbing
Climbing is a fun and relatively safe sport, but there are always some risks involved. As soon as you step up from the ground, there is the obvious risk of falling back down again. When you climb with ropes, it's the job of the belayer to make sure you don't reach the ground if you fall. However, accidents can and do happen, even if they are rare.
In top rope climbing, you might swing out from the wall and hit something if you fall, so be aware of your surroundings. In lead climbing you will always fall the distance to your last quickdraw, plus the same distance past it. If you are too close to the ground or too far above your last quickdraw, you might hit the ground before the rope catches you. You might also hit things on the wall on your way down, like ledges, or things sticking out of the wall.
Statistically, virtually all accidents in non-alpine climbing are due to user error. They are caused by the climber or the belayer making mistakes, like having too much slack in the rope, or forgetting something. The vast majority of these accidents are avoidable. If we learn safe methods for belaying and always do a partner check before climbing, we can avoid many of these mistakes. Never put your fingers through bolt hangers or other hollow objects on the wall. Having a finger through a metal ring with sharp edges is not great if your feet slip off the wall.
Also keep an eye on where you place your feet when you're lead climbing. Never put your feet between the rope and the wall. If you fall, you risk being flipped upside down by the rope, possibly hitting your head on the wall as well. Always step around the rope on the outside of it when moving around.
Risks involving equipment
Accidents caused by your equipment failing are exceedingly rare. Ropes, harnesses, carabiners, and everything else we use for climbing are made to be super strong. They are all able to withstand much higher forces than you can subject them to in normal climbing. The few ways you could manage to break any gear would all involve using the gear incorrectly. You might break a carabiner by hanging it right on a sharp rock edge and then loading it sideways. You might cut a rope by moving repeatedly sideways, rubbing a rope across a sharp edge. Be aware of these risks, and you will almost always be able to avoid them fairly easily.
You are insured
As a participant in one of Surmount's courses, you're covered. I have been an instructor since 2016, and I have so far never had any kind of accident in any of my courses. Safety is always my first priority. If by some weird fluke something were to go wrong anyway, you are insured. I have an insurance for my participants that will take care of medical bills and many other things.