Wow, that is very close. You are quite lucky. I hope your insurance can cover the damages. We had a tree branch fall like that back in 2020 ourselves. It was quite scary. Our dog just barely made it back inside the house before it fell. She would have been seriously hurt otherwise. My wife was home alone at the time and it definitely traumatized her a bit.
It's quite amazing how heavy and dense these things are! Insurance covers our end and we will pay the excess for the neighbour. The insurance companies can be really nitpicky about what is and what isn't covered.
Yes they can. It is pretty ridiculous! We had a tree taken down preemptively and it cost us $2000.