1. More thank likely if a shop goes down there is something going on on their end.
2. No. At one point some shops broke after Tinfoil got an update, but that's because the author changed the way Tinfoil connects to servers. It was a 1 second fix for shop runners to make their shops compatible again. There is a certain shop (that I cant mention because rules) that requires you to use their tinfoil theme for some reason, but that's just a visual thing. Tinfoil runs on all FW versions and auto updates itself by default so you will always have the latest version unless you intentionally turn auto update off. (which you shouldn't)
3. No. Odds are is if a shop goes down, it's probably because they either don't want to run the shop anymore, or they got taken down by the storage provider and/or Nintendo, in which case the ones running the shop may decide not to bother starting from scratch.
4. Paid/Pro shops are the primary source of all the games that are available to pirate as of now. When you donate to get into a Pro shop, you are donating an eshop code which is when used by the staff running things in cooperation with missingdumps in order to buy and dump games that have yet to de dumped, are nice and would not be dumped otherwise and so on. When you donate and use a pro shop, you are helping everyone else have access to as many free games as possible. Most of the public shops as of now are either run by the same groups that run the pro shops, as a free option who either cannot afford or are hesitant to, donate to a piracy effort. The ones that aren't run by those groups, are basically just leeching downloads they got from a torrent or from one of the pro shops even, and are doing it to gain some glory and clout without having to contribute to the scene. Some do it out of spite and vindictiveness because they don't like the idea of money changing hands for piracy, as it threatens their little ego trip and sense of identity as a "1337 h4xx0r" that can get anything completely free.
Pro shops are easier to use. The current free shops require you to go through a bunch of rigmarole in creating an OAuth token in order to be able to actually access and use the server through Tinfoil itself. Pro shops are more plug and play. They give you login info, you enter it into tinfoil, and it just works.
Free shops owe nothing to nobody and can at any time take their ball and go home, leaving you out to dry. Pro shops have a vested interest in keeping their service running as for as long as possible and with as much uptime as possible simply because a financial investment has been made on not just the part of it's users, but on the part of the people running the shop, and they tend to be privately hosted instead of using free cloud storage like Google Drive the way free shops tend to. When all the free shops are dead and gone, there is a reasonably good change the pro shops will still be kicking. It's up to you to decide if that kind of reliability and convenience is worth a one time minimum donation of $5 US.