This is a topic I can indeed talk about at length. Here's the TL;DR version: I bought a new 2019 Sprinter 4x4 170" wheelbase, had it custom built by Van Life Customs in Denver, and began living in it full starting in July of 2020. I very recently bought a house (less than a month ago) but will still be doing the #Vanlife, Everywhere dirtbag thing often, especially in summers when climbing is better. 11/10 experience, would do again.
The longer version could get very long so I'll answer the questions in the OP as briefly as I can:
Showers: I don't have one in the van. I bathe in creeks or lakes when it's warm enough, at friend's houses when I can (so far everyone has been very nice about it, it makes a great excuse to see friends more often, and I don't abuse the kindness), and extremely rarely at truck stops, literally twice ever. I don't think I ever went more than a few days without a cleaning, except in winter when I'm not getting quite as dirty and sweaty in the first place. A shower is a huge waste of space and water in a vehicle and prone to leaking and making a mess.
Toilet: I also don't have one, that's what the woods is for. I always try to park in places where there's either a public restroom (BLM areas, Walmarts, etc.), somewhere I can easily walk to a bathroom, or somewhere I can get out of sight of the road to do my business. I do have a pee bottle and it's the most convenient thing ever at night or when trying to be stealthy (and not get arrested, but that's another matter). A toilet is a waste of space and smells bad, so plan accordingly and there won't be any problems (mind you I don't have any digestive issues like IBS).
Water: water is by far the biggest problem you will encounter. I have a 20-gallon tank for running water that I can stretch into about a week and a half to two weeks if I don't cook very much, since cooking and washing dishes tends to use more water than any other activity. I started off cooking a lot since I like to cook and quickly realized I was blowing through my water in about six days even if I was being extremely careful. Then you have to find a place to fill up, which I hated paying for. That wasn't the freedom I sought in the first place. It's usually cheap at RV parks but there are places that will let you fill up for free. Finding those places and making use of them is another consideration to always be mindful of. If you don't have a dedicated water tank like I do and have something like jerry cans that probably means you're in a smaller space and generally unlikely to be cooking as much or doing the "extended" stay thing. I know Whiley, who lives out of her truck in the summers, uses jerry cans and just buys large bottles of water every so often to refill. In winter your water is likely to freeze even when you have a heater. My tank is under the bed so it doesn't get much heat back there and I've had burst pipes and even destroyed a water pump when it froze solid. I'll get into winter living later on.
Internet access: I do IT infrastructure and was remote for years before the van so there was no huge shift there, and because my work is of a somewhat security sensitive nature my work provides me with a dedicated Wifi hotspot, a Verizon Mifi. It is cell-based so I have to pick my camp spots somewhat carefully, but just like places to poop that's a consideration before I stop overnight. I spent 95% of the summers of 2020 and 2021 in the San Juan where cell coverage can obviously be spotty but had no problems working full-time. If a spot didn't have coverage I'd just wake up a little earlier and move into town, nobody messes with you during the day. Satellite internet works everywhere but it's slow and pricey. If you plan to spend the majority of your time in official campgrounds, which are sometimes fairly off-grid and I think are a waste of money, or you plan on not moving around much, then perhaps satellite would be ideal.
Entertainment: I don't have a TV in the van and haven't owned one in probably 10 years. In a vehicle I think it would be a waste of space, just use your computer. I read a lot and play some games, mostly single player. If you want to be stealthy get a nice, comfortable, noise-canceling headset.
Stealth: you will be hard pressed to be stealthy in anything smaller than a full-sized van or other vehicle with dedicated living space (very easy to see someone moving around inside the cabin of their truck, for example) and if you actually want to be stealthy don't overdo the outside of your vehicle. I have a ladder on the side of mine to access the fan vents and solar panel on the roof but aside from that no other indication that someone might be living in it nor what might be inside - no seventy billion herpa derp climbing stickers that basically tell the world you have expensive gear inside and are probably a dirtbag. I bought window shades for every single window as well as magnetic ones to seal off light and cold from the roof vents. They weren't cheap ones, they were custom made to block out every bit of light and they work I'd say about 99%. This is huge when sleeping in town. Nobody knows I'm in there. I could very well be parked there seeing a friend, they can't prove I'm in there. I have never once gotten a knock from the cops and aside from one incident where I parked in front of someone's gated driveway at night, accidentally blocking them in, I've never had anyone even know I was there. I try to park next to large trees or fences when I can. I do have a handgun for those areas I don't feel quite as safe but that's rare.
Winters: this is what drove me to buy a house. Winters living in a vehicle, even with a dedicated heater such as mine, absolutely suck. Poor daylight hours, not as much to do, more difficult and dangerous driving, less opportunity to get clean unless you want to pay for it, harsh isolation, you name it. I've got a dedicated diesel heater since my van is diesel and it struggles to keep up when it dips below, say 20. When it gets to 0 I'm sleeping in a jacket. When it got down to -20 like it did in February the diesel gelled up and I spent an extremely miserable few hours with no heat before a friend bailed me out and let me crash at her place in Denver. Had I been farther away I probably would have had to get a hotel. I cannot overstate how much I struggled living in the van in the winter, and that's coming from someone who likes the cold, likes sufferfests, and generally doesn't like people, and it was still rough. I could certainly have gone farther south to warmer climates but I'm working on 14er snowflakes as well as a bodysuit tattoo and my artist is based in Denver, so I have to be around regularly to get inked. If you don't have similar constraints I highly recommend going somewhere warmer. Potrero Chico in Mexico is amazing as hell if you can swing it.
4x4: honestly, probably not necessary. I got it and have made extensive use of it but it's by no means necessary. On my Sprinter it was about $10,000 extra for 4x4 and I bought it 51% for driving in snow and 49% for accessing more trailheads. I ended up doing significantly less driving in the winter and while I have definitely taken my van to places I probably shouldn't have, like Cinnamon Pass, Stony Pass, and Endlich Mesa, I grew tired of abusing the hell out of my literal home so I stopped trying to drive as close as possible to my peaks and just tacked on extra road miles when it wouldn't be absurd to do so. Keep in mind I bought the middle-sized Sprinter (there's 144" WB, 170", and 170" extended - watch that overhang in the back!) which is 23 feet long and about 10 feet tall, so there are plenty of places you simply cannot take a vehicle of that size no matter how ballsy you are as a driver, but considering I live(d) in my van I chose space and comfort over access. At some point I'm going to buy a dirtbike and use that for upper trailhead access, at which point the 4x4 will be used very rarely. A smaller vehicle is going to offer you a LOT more accessible options, but considering I've done like 400 13ers since I bought the van it's really just a matter of conviction and having friends with appropriate vehicles (thank you, Whiley!) more than technology.
Buying new vs used: I bought new because it was really my only option for getting 4x4, and I didn't want a van with 250,000 miles on it. That was an easy choice for me and I had the money for it. If you don't have the money, well, you're going to be buying a beater, probably. I bought the van from Jim Plank at the Westminster dealership. He's great, but the process not so much. It took me almost a year to get a 4x4 due to high demand and that was pre-COVID. I often didn't know when the van was coming and Jim didn't either because apparently the new factory Mercedes built in Texas or wherever is a total shitshow. I can't imagine how bad things have gotten or how long the line is now with COVID, so be aware you're possibly looking at several years before you get something.
Custom vs pre-built: Again an easy choice for me since I went custom, BUT I did do extensive research on all of the available pre-built models of camper vans such as Winnebago, Sportsmobile, Outside Van, etc. Only one or two companies offered 4x4 Sprinters and they were ridiculously expensive; I quickly came to the conclusion that I could get more van at a lower price if I went custom (for example, the Winnebago Revel was $144,000 two years ago and only comes in the 144" WB size. It's very cramped. I got my 170" WB factory new and customized it for way less than that). I also extensively researched companies that do conversions and Van Life Customs in Denver made the rest of the competition look like garbage in comparison. The only other real competitor was Outside Van based in Washington and I wasn't a fan of their styling and less a fan of their pricing. VLC, on the other hand, let me do pretty much anything I wanted, was a bit softer on the styling, closer to my then-home in Boulder, and was less expensive. I'm going to give a plug to the Van Life Customs guys, they are AMAZING. Seriously. Incredibly nice, so full of good ideas, beautiful, quality craftsmanship, they're the real deal. I basically came to them, told them the vision I had, and they helped put together a plan and then made that plan reality. To say they exceeded my high expectations is a huge understatement. This isn't a post about them, but they were able to fulfil my very high requirements, something like several pages worth of requirements that I wasn't sure were realistic or possible. Would I have gotten the same level of quality and service and customization from something pre-built? Not a chance. Easy choice going custom. You could also do it yourself if you have the skills but I'm a computer nerd and knew I couldn't do this on my own so I didn't even bother.
Other: you'll quickly find out all kinds of stuff can and does go wrong. Be prepared for messes you never expected (things flying out of cabinets while you drive? It'll happen. Ever end up with multiple shattered bottles of spaghetti sauce painting the inside of your vehicle? I have. It sucks.), miserable times, broken parts, harassment, questioning looks, but also for some of the best times you've ever had. The last two years have been undoubtedly the best two of my life. I was very well prepared for this life, having spent up to 4 months straight living out of a Civic for several years in a row, so if you aren't completely on board with this then make sure you get on board. Deliberately make choices that will prepare you for living in a small, mobile space, because it is nothing like even living in an apartment, nothing. But would I do it again? 110%.
Ok that was a lot longer than I originally planned, but I hope this is helpful! There are other site members who live out of their vehicles - Whiley and Justin Sendtek come to mind - so I hope they'll chime in too. If anyone has questions feel free to ask!