I mean, the old 5/8 inch regular board never sagged like this new stuff does, at least in my experience.
I always thought my son was too distracted to help with drywall. But last week, he pointed out a stud that was out of plumb before we hung the board. That saved us from having to redo a whole section. Now I see that fresh eyes, even young ones, can be really helpful.
Put a thin layer of mud on the tear. It gives the tape a good surface to stick to.