I've just started laser hair removal myself (had my second session a couple of weeks ago), so although I'm still a bit of a newbie I can hopefully answer some of your questions.
For context: I am Asian, so have dark skin and dark hairs, so it definitely has to be laser for me (not IPL), and it has to be a certain kind of laser (ND:Yag) for it to work effectively. As far as I understand it, IPL is more effective on fairer skins and lighter coloured hair types, and laser would not be as effective. I had to do quite a bit of independent research before I took the plunge because there is a lot of differing advice out there, so I would advise you to do some research before you even go anywhere near a salon, and even when you do, go to a few salons and get consultations from all before committing. Once you've done some research based on your own skin type you'll soon be able to see when someone is spouting a bit of bullshit at you to make a sale, and/or when the same professional advice is being regularly given by reputable salons. I don't necessarily believe that salon 'names' matter as much as their technicians and the lasers they use, but of course, bigger brand name salons tend to (you would hope) have professional accreditation as well as strong reviews from customers. I go to a fairly well known salon that specialises in hair removal services.
Laser works like this: the day before a session, you have to shave the area that you'll be having lasered. So for me that's my face and chin. You can't wax, thread or pluck it, because that would defeat the whole purpose of the exercise. Those methods pull the hair out from the root. Laser works best for hairs which are in the anagen phase (i.e. when the hair is still attached to the root). Not all of your hairs will be in the anagen phase at the same time at any given point, so that's why you have to do a number of sessions in order to see good results - it's about making sure you capture as many hairs in the anagen phase as possible. They advise 6 - 8 sessions minimum; I've signed up for 12 on the advice of my technician.
Laser will then destroy the hairs in the anagen phase, and as the cycle continues through the month, the hair will detach itself from the follicle and start to shed. In a 'normal' (i.e. non-laser) cycle, this would be the point where a new hair would start to grow from that root, but the laser destroys the hair bulb itself so that eventually it stops producing new hairs.
Once you've had the session, you have to leave the hair to grow as it normally would. I won't lie - this was one of my biggest concerns, because, with my hair being as dark as it is, I would get very self-conscious going to work and about my daily life with that much facial hair. With waxing I would only have a two week wait and in between I could pluck any obvious stragglers, but with laser I have to wait a month at least for my next session. So the first time I had the session, my hair grew back as long as it always would and I struggled to leave it alone. You have to do it, though, otherwise - again - it defeats the purpose. Anyway, ten days after the laser session, you shave that hair again, and this is the point at which the hair starts to shed. If you exfoliate regularly you'll start to see small hairs shedding with dead skin. It's weirdly exciting to watch this happen (at least the first time!) because you can tell it's working. Then, you repeat the cycle, and shave again the day before your next appointment.
So, you: Shave 24 hours before > Have Laser > Shave 10 days after appointment > Hair starts to shed > Shave 24 hours before next appointment.
Since my second appointment, I've noticed that my hair has already stopped growing as much, and that it takes a little longer to grow out than before. I don't want to make this out to be some miracle cure that will work the same way for everyone - I think for me, the years of waxing probably contributed in some way to lightening the hair enough for this to work so quickly, and I'm still going to go through all 12 sessions that I've paid for, in order to make sure it sticks.
To put this all in perspective, before embarking on the laser journey, I have had my face and chin professionally waxed (and eyebrows threaded) every two weeks for at least 7 years - regularly. Not only is that expensive (and painful), but it was a fairly heavy maintenance schedule. In between, I would pluck any stray hairs that couldn't wait until my next wax session. Each session would last about 45 minutes. With laser, I have to shave my face the day before, which is not painful and doesn't take that long at all, and then on the day, the session itself takes 15 minutes start to finish (this probably varies from customer to customer, but I don't think it takes nearly as much time as a wax does). Then, nothing for ten days, when I shave again. In all honesty it's been such a relief to go from a heavy 45-mins-every-two-week-without-fail cycle to a relatively light one. I go in for a 15 minute session once a month and then essentially forget about it.
Pain-wise, I'd say that laser definitely does sting, but for me, not nearly as much as waxing and/or threading. The laser is hot and accompanied by a very cooling fan they place on your skin at the same time, which is a bit of a weird sensation though not necessarily painful. The laser itself feels like a hot pin-prick, and technicians usually work fairly quickly across your skin, though they will adjust the speed if you prefer. For me it's most painful around the chin area, and that's because my hair is thickest there, but it only lasts a minute at the most and they only go over the area once so when it's done, it's done.
Afterwards, you absolutely have to wear sunscreen, every day. Without fail. No matter where you live. Particularly the day of/couple of days after the treatment, but they are very insistent that you wear it regularly. They also advise the use of aloe vera gel for any redness or bumps that may occur. I have - so far - never experienced rashes or redness. When you go in for a consultation they will do a patch test so you can be sure that the laser won't produce any major side effects, but I'm told that occasional redness immediately after a session is normal and to be expected. You have to be careful re: going on sunny holidays/tanning etc. If you have a tan, they will ask you to push your next session back until the tan has subsided; this is something to do with the effectiveness of the laser beam on tanned skin.
I can't advise on the peri-menopausal thing, other than to say that, since the laser targets the hair follicles that exist (and are in anagen phase), going through the treatment now will presumably still work in the same way as described above, and it's about deadening the root (bulb) of the hair more than it is about any hairs that are above the surface. Salons and experienced technicians would definitely be able to advise you on that when you go in for a consultation though.
I don't know about the dark spots thing - luckily I have not experienced these at all. I would say that (having done this myself!), a lot of the pictures online can be off-putting or even misleading, but you have to remember that there could be any number of reasons why they have those dark spots - they could have used the wrong lasers, or their hair type or growth is different, or they have unknown hormonal issues, or whatever else. Everyone's skin is different, and the hardest thing is to know exactly how laser would affect yours. It's why it took me years and years of dithering before I finally took the plunge. I wish there was a more cohesive industry standard re: laser hair removal but until there is, we just have to inform ourselves as best we can and not be afraid to ask as many questions as we need. I went to a couple of salons before I picked mine, and luckily consultations and patch tests are (generally) free, but I took my time choosing the salon I did, and you have to be confident that the technician and/or salon is one that you are comfortable with.
This turned out incredibly long but I hope it helped answer some of your questions!