Juvenile Justice was really great, but it's hard to say why without getting into spoiler territory. Let's just put it down to overall character development.
I can reach it just fine. Maybe you need to flush your cache / DNS?
Generally speaking though, unless they have provided alternative means of contact and you saved them prior to the outage, there's nothing you can do. Same if they decide to shut down - the instance and your account would be lost, and that's that.
Edit: you can look up the owner of the domain on sites like https://who.is, but more often than not they use anonymizer services to not reveal their residential address. The given email address there might however serve as a forwarder to their actual one.
Using a dedicated browser should be good enough. Since you might need some proprietary google stuff, I'd suggest chromium portable, that way once the class is over, you can simply delete the whole folder and call it a day.
On mobile I'd suggest Fennec instead of stock Firefox since you can use add-ons without limitation, and don't need workarounds such as the Firefox nightly.
It's basically stock with enabled add-ons, and following the official release cycle with 2-3 days delay. Maintained by the original developers of the F-Droid store, so also a highly trustworthy source IMHO.
Reminds me of the movie "I origins" (the maternity ward part). If you haven't seen it, it's one of my all time favorites - and better to be watched without knowing what it's all about, too easy to spoiler.
All of them. I'm browsing /all simply to block more, so that they won't accidentally show in my feed.