In my circle of friends/family/neighbors/acquaintances, it's common to have a vehicle over 200k miles. Over 300k is noteworthy but not unheard of. Both of my cars are over 275k (bought them a little before the 250k mark).
One guy I see regularly is driving a 400k mile minivan. At my previous job I saw a customer driving a 500k mile Corolla, as well as a couple of customers with 400k, and countless over 200k.
I received the car at about 370k miles, drove it about 10k more for ~2 years in college. The only problem I ever had with it was the battery sucked in the winter.
Nope. That's mostly (I guess?) an issue in places with a lot of winter months that use salt on the roads instead of sand. It's had a bit of rust, but nothing a buzzbox welder and some steel sheets couldn't patch.