Yes. They are not trivial to distinguish from other large industrial buildings. If you know a building is one, you still don't know whose.
It's local public knowledge. The buildings are registered with the county they're in and pay taxes. In the US at least, that's public info.
Odds of data centers being physically attacked at scale are low. Most of the population doesn't care enough, and the vocal minority is under a lot of scrutiny.
Except from the massive power hookup, all the cooling equipment, and the emergency generators, of course.
You can hide a handful of racks for some boring 2000s hosting. You can't hide a GW-scale AI behemoth.