Depends on who you ask, for me, they count as both climbing and training.
I have a MoonBoard at my gym, and I usually prefer to climb on it rather than training on a hangboard. Though I do have at least 1 session a week for hangboarding and campus runs, I do prefer to climb on the MoonBoard because it's just more enjoyable compared to just hanging off of an edge. On a MoonBoard, you are also training crimps, and pinches, and you are also just climbing. Not to mention that you also train your core and back and other muscles while doing it, in comparison to hanging on a hangboard, where you train mostly your fingers, and just hang.
So for me, it is training, and it is also climbing, even though the climbing on it is very different from climbing on a regular climbing wall, but every so often you get a boulder route that is very similar to a MoonBoard problem, and if you climb regularly on a MoonBoard or other board wall, those routes will be much easier.
When you start to see a hole in them, and before the hole goes through the fabric of the shoe, otherwise it will just cost more to get them resoled and to fix the hole in the fabric rather than just resoling them.
The most common place for holes is in the front tip of the shoes, where your toes are. This is usually due to either poor footwork, or just the lifespan of the rubber on the shoes. Softer shoes with soft rubber tend to wear out faster. Once you start to see a hole, you may have a few more sessions left before the hole really becomes bigger. Waiting too long though can just cause the hole to expand and eventually there will be a hole in the actual fabric of the shoe, which usually is also fixable, but just costs more.
Sport cloths, nothing special really. Depending on the gym you will be climbing at, you may have to wear climbing shoes, which are usually provided at the gym as rentals. Chalk bags are also usually provided or can be rented for that session.
Other than that, something comfortable would be best. If it will be your first time, or you are a beginner, long pants may be wise to help prevent leg scratches if you slip or hit a climbing holds. They can easily scratch the skin without you even noticing.
Your lats and your back would do most of the work while climbing.
Something beginner climbers usually experience is that sensation of discovering "new" muscles in their arms. These are just muscles that they have not used before, or not as often as they do in climbing. Many may think that this means that your arms are the most worked muscles in climbing, since they hurt the most, but, it's just because they are normally not utilized in the same way as they are when climbing.
Your back muscles, on the other hand, are those which actually pull you up. Your arms are used for keeping you on the wall, but what lifts you up, other than your feet which should be pushing you up, are your lats and back muscles.
Think of it like a pull-up. You can hang from the bar for quite a while, but, the moment you start to lift your self up, and do this repeatedly, your back will begin to slowly fail, as it is the back muscles that are bringing you up.
Bent climbing shoes are called aggressive climbing shoes. They are bent, and many times also have a curve in the direction of your big toe, to give you more power when standing with your toes on small edges, and to give you more pulling power with your toes. Imagine a piece of paper on the floor in front of you, put the tips of your toes on it and pull it towards you - aggressive climbing shoes make it easier to pull your body weight like this on climbing holds, they allow you to pull yourself closer to the wall and keep you there.
The bend helps you engage more and put more force onto the tip of your shoes, allowing you to add more tension and be more stable on tiny edges that otherwise could be very difficult to stand on.
Aggressive climbing shoes are also great for overhanging climbing, since the added tension and force you can exert with your toes can help you keep your feet on the wall, which prevents you from cutting loose and hanging from your hands, which can be very tiring and costly and could cost you finishing the route.
Part of a rock climbers training is to be able to climb for longer periods of time. They do this by doing endurance training, which allows them to scale up very tall walls and long routes.
This also comes in to play with bouldering. Climbers are able to have long 3-4 hour climbing sessions by resting in between routes and attempts. The amount of time each climber rests depends on the climber, their endurance, and the route being climbed.
Generally, it's not abnormal for climbers to spend over 6 hours climbing. It's just the nature of the sport. Climbers are not constantly exerting energy the whole climbing session, they are resting enough time in between attempts to allow them to make the most out of each training session.
Even when climbing a big wall and a long route, climbers are able to find certain spots on the route to rest. And this is where climbers excel. Climbers can find spots to rest mid-route that would seem impossible to non-climbers. These spots could be very small hand holds, but for a climber, this could be all they need to recover some of their energy, reduce the pump in their forearms, and continue climbing.
You can walk in climbing shoes, it is just not recommended. Climbing shoes are not meant for walking, they are meant for climbing. Walking in them can just wear the shoes out quicker. Not to mention that they are also pretty painful to just walk in.
A lot of climbers like to walk in new climbing shoes to help stretch them out and break them in, so that could be an exception to the above. After those shoes have stretched, though, it would just be wearing them out quicker.
I usually put a vitamin E cream on them.
There are creams and balms that are made specifically for climbing, but I have always benefited from pure vitamin E. I haven't tried any of the others climbing specific creams or balms, though.
I have a cream that is very heavy in vitamin E, I put it on either the same day after climbing if I remember, or a day later, and it recovers my skin pretty quickly. After an intense bouldering session, my skin can be left pretty thin and sensitive, after I put the vitamin E cream on though, it feels much better and is ready for another session.
There are also vitamin E oils, which may have better results, but are messier. They are probably best applied at night before going to sleep, that way you don't touch anything with the oil. Another option is to put on finger gloves that cover just each finger, this way the oil doesn't touch anything.
