I had a vehicle that had several of these problems. It was a mini-van and it would bottom out all the time. I have friends that I would visit and I would avoid parking in their driveway, because I would bottom out every time I left. It didn't happen to anyone else though.
The van also swayed really bad when I would turn. I thought it was just old and falling apart, but I live in an area that gets a lot of really bad potholes every winter. I've definitely hit quite a few of them, so maybe that's what caused these problems on my van.
I have a different van now, and I'll be sure to pay more attention to damage that could result from potholes. And, more importantly, I'll try better to avoid the potholes in the first place!