A climbing shoe normally feels tight, snug, and applies a certain amount of pressure to your feet. This is especially true with new climbing shoes, as they have not yet been broken in. If the shoes are synthetic, they may not have a noticeable break in period, and however tight and snug they are when you buy them, may be how they feel even after a few months in them.
The same climbing shoes in the same size may also feel different for different people, as people have different shaped feet. The same shoes that may be applying a lot of pressure on your big toe, may be causing someone else some pain in another area of their foot. Everyone's feet are shaped differently and have different characteristics, so not all shoes will fit everyone the same, but, you do get used to most of the pressure after a short while.
Once you get used to wearing climbing shoes, a lot of the slight pains, discomforts, and other pressure points start to fade, and your feet get used to them.
You do not normally need to force the break in period of climbing shoes, this will happen naturally by wearing the shoes and climbing in them.
There are of course different methods for breaking in climbing shoes faster, but, they are optional and not required. Some methods could even be harmful for your shoes.
Whether your shoes need to break in or not depends on the type of shoes you bought and the size. If you bought shoes that are synthetic, don't expect any noticeable change even after 6 months of climbing in them, since synthetic shoes don't really have much of a break in period, and if they do, it's very minimal. This should also be a determining factor when buying climbing shoes, since you probably won't want to size down synthetic climbing shoes, expecting them to stretch.
Leather shoes, on the other hand, do stretch quite a bit, so if you bought leather shoes, and you sized down, then you should expect a break in period.
Rock climbing shoes that are too tight can potentially cause damage to your feet, some of the most common being muscle pain and bunions.
Climbing shoes should be tight and snug, but not too tight. Climbing shoes should not cut off or reduce circulation to your feet, and should not cause lasting pain even when taking them off.
Wearing climbing shoes that are too tight can also be dangerous from a usage point of view. If you fall from a route or jump down, landing on your feet, due to the stiffness of your muscles, they may not be able to absorb that impact as well as they should, which could cause damage.
The key to reducing the possibility of damage and pain is to choose climbing shoes that actually fit you and the shape of your feet.
It depends on the type of shoes and their purpose. Synthetic climbing shoes may stretch up to half a size, and even that is not very common. Usually, there is no noticeable break in difference with synthetic shoes, which means that if you go down a size in them, and they are very tight and painful, that may be how they will always be.
Leather shoes, on the other hand, do tend to stretch, and can even stretch up to 2 whole sizes, some even say more. Because of this, many climbers go down even 2 sizes.
It's normal and quite common for new climbing shoes to hurt a little bit. With that said, they should not cause throbbing pain that lasts after you take them off.
Depending on the type of shoes and their material, new climbing shoes usually have a break in period, which can take a few climbing sessions to get through. During this break in period, your shoes will start to change in shape and fit, molding themselves to your feet. This process can be very uncomfortable and a little bit painful, depending on the size you bought.
Keep in mind that this break in period varies depending on the type of climbing shoe, the material it is made of, and the size of the shoe. Synthetic shoes may stretch at the most half a size, while leather shoes can stretch up to 2 whole sizes.
If your shoes are synthetic, and they are causing you pain, keep in mind that they may not actually have a very noticeable break in period, which means they may just not be right for you. You may also not be used to wearing climbing shoes that are tight, which also takes time to get used to.
For warming up on the wall, many climbers like wearing slightly looser shoes. This is to give their feet time to also warm up, but also to not have to warm up with the pressure from the tighter climbing shoes.
If you are climbing hard routes or projects, you will most likely benefit from tighter shoes that have little to no dead space in them.
If you are a beginner climber, it won't make much of a difference, and you should probably stick to slightly looser shoes. Tighter climbing shoes can provide extra performance advantages for climbers climbing difficult routes. If you are not climbing difficult routes, and you are a beginner, you most likely will not even notice these performance gains from the shoes, as the routes you are climbing do not even utilize their benefits.
Yes, your toes should be slightly curled in climbing shoes.
Having curled toes allows you to exert more force from your toes. This is especially helpful when you have to stand on small edges, or to even jump from them to another hold.
Though they should be curled, your toes should not be in pain. If your toes or feet are in pain, the shoes may be too small for you, or the shoes may not be the right shape for your feet.
Climbing shoes, after their break in period, should not be painful to walk in, but they can be uncomfortable, tight, and snug.
During a pair of climbing shoes break in period, they may be slightly painful, but should not cause too much pain. After their break in period, they should have stretched enough to not be painful, while still remaining tight and snug.
If you have been climbing in your shoes for a few sessions, or a few months, and they are still painful, you may have just not bought the right shoes for your feet, or they may just be too small.
Usually the break in period can be around 5 sessions, for some it may be more, but after a month or two or regular climbing, they should be broken in.
Climbing shoes should be snug and tight, but not too small. What that means is that there should be as little dead space in the shoes as possible, ideally, none.
Climbing shoes are designed to be snug and tight, and to not have dead space within them. But, climbing shoes come in all shapes and sizes, and not all shoes will fit every climber. This is why it is important to try on different shoes and different sizes in order to find the right pair of shoes for the shape of your feet. The right pair meaning shoes that are snug, have no dead space within them, and fit the shape of your feet also in terms of the toe box and how wide it is.
Whether climbing shoes should be bigger or smaller depends on what you are comparing them to. I personally wear half a size larger than my street shoe size in all my climbing shoes. I have a very difficult time finding shoes that fit properly, especially in the heel area, and I find that going up half a size is even a semi performance fit, as going down is just unbearable.
So you can go down in sizes or even up, as long as the shoe fits the shape of your feet, is snug, tight, and has little to no dead space, and most importantly, is not too small.
If it helps, I wrote an article on this very subject on this site's blog, it goes over all the steps for choosing the right climbing shoes for your feet: Climbing Shoes 101: How To Pick The Right Pair For You
There isn't really a correct amount of shoes you should have. Some people have just one pair, while others may have many. More experienced climbers tend to have at least a couple of shoes, and professional climbers usually have quite a few shoes.
The amount of shoes you should have does not necessarily depend on your climbing experience. Professional climbers have many shoes because they actually need them. They go through their shoes quite quickly due to all of their training and competitions. Climbers who are not professional climbers, but are more advanced, sometimes end up having a few shoes because they just bought them with time.
If you are just starting out, just having one pair could be more than enough. Some like to have a pair that is used only for warm-ups, and another that is used for their harder climbing and projecting. Some climbers also like to have 2 pairs of climbing shoes so that if one pair is being resoled, they can still climb with the other pair.
Some buy shoes because they are on discount also.
In the end, it depends on your needs, and budget of course. There is no general correct amount of climbing shoes a climber should have.