Safari shut down my Mac

That sounds like a Kernel Panic: If your Mac restarts and a message appears - Apple Support

It is not normal and should not happen, and might never happen again. If it does though, post a copy of that KP report in a reply. It does not often reveal anything you can fix, but on rare occasions it could be helpful.

In any event it is not any indication of something nefarious going on.

Safari cannot shut down a Mac no matter how hard it tries.

How do I check if I have been hacked?

Describe the reason for your concern. If someone or some thing has established remote control over your Mac, it can do everything you can do as you sit before it.