It has been years since I went bouldering or climbing, and I was not an expert by any means. However, I am an expert at Not Breaking My Glasses, and like you, not wearing them is not really an option!
2) At the heights from which you would be falling, presumably onto mats, I would be impressed if you managed to break your glasses. Modern glasses are very durable (I've dropped mine on concrete and other hard surfaces many, many times. They get a little scratched. Sometimes the frames get a bit wonky and have to be adjusted. I have never broken a pair.). Hopefully you would not actually fall on your face (ow), and if you're concerned about your glasses falling off and breaking from the drop, or from you falling on them, you could wear a cord or one of the floaty things sold for water sports. I'm not sure I would bother unless you often have problems with your glasses falling off; I know mine have stayed on through much bouncier activities than falling off a climbing wall.
As far as 1) and 3) goes, this may vary by gym, but the gyms I used to climb at, you just showed up and went for it.
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2) At the heights from which you would be falling, presumably onto mats, I would be impressed if you managed to break your glasses. Modern glasses are very durable (I've dropped mine on concrete and other hard surfaces many, many times. They get a little scratched. Sometimes the frames get a bit wonky and have to be adjusted. I have never broken a pair.). Hopefully you would not actually fall on your face (ow), and if you're concerned about your glasses falling off and breaking from the drop, or from you falling on them, you could wear a cord or one of the floaty things sold for water sports. I'm not sure I would bother unless you often have problems with your glasses falling off; I know mine have stayed on through much bouncier activities than falling off a climbing wall.
As far as 1) and 3) goes, this may vary by gym, but the gyms I used to climb at, you just showed up and went for it.