No. It’s not a magic invisibility field inside. It’s a magic object that works only on living “intelligent” creatures. It also doesn’t work the same on different races. Only humans (hobbits are a subtype of human in Tolkiens lore) turn invisible. And because it’s magic it also turns their clothing etc invisible. So either Frodo and his poop is invisible or nothing is.
The western hemisphere isn’t just the Americas. It includes half of europe…
There are quite a few people in the western hemisphere that don’t even bat an eye when they walk past a 1000 year old building on their way to work every day.
For me the oldest building is just a random house from the 13 century.