Have you had other solid counter tops? Formica counter tops are set in from above and (generally) don’t have the ability to fall through.
Yes, the garbage disposal would likely have to be removed to do any work on the sink. Especially, if the sink needs to me moved more than an inch or two. However, after you’ve removed/installed one more than once or twice, you can do it with your eyes closed. It’s literally one plumbing connect that’s usually hand tight and one connection to the flange on the sink that can be done with the tool that comes with it. The dishwasher and electrical connection can stay attached. Dropping the disposal takes 5 minutes.
As for how the sink is attached. I’ve never set one in like that. I know there’s clips, and clearly yours broke, but if it were me, I’d find out if the best practice/industry standards involve using an adhesive as well. If they do and if that step was skipped, yeah, that’s on them to ‘make you whole’.
I think you need to see how much, if any, water damage there is. If you can dry it and nothing is damaged. I’d probably get them to fix it and be done with it, assuming they do it right this time. If there’s damage to the cabinet, I’d hound them to take care of that. It was damaged due to something they did incorrectly, it should be on them to repair it. If they put up any resistance, you might say something like “I paid $xxxx for this, I shouldn’t have to pay more because if failed and caused a bunch of water damage.”
Worse comes to worse, fix it yourself or have another company come and do the repairs and take them to small claims. Either they’ll pay for it or you’ll be out 60 bucks for trying. Personally, I’d take the risk.
BTW, take pictures (the fallen sink, broken plumbing water damage) and document everything (phone calls, what you/they said, what steps you’ve taken etc) before you do anything.
PS, I don’t want to victim blame, but once it starting failing, you probably shouldn’t have used it anymore. However, if they mention that, play dumb. Just say 'I don’t know anything about plumbing, I called you as soon as it happened, no one said anything about not using it anymore."