You'd be surprised how big some of the Mars rovers are. Curiosity is about the size of a car.
As far as research...absolutely yes they would want to go there for research. There are caves on Mars that are nigh on impossible to explore with current technology, and that could hold some very valuable information.
Interestingly, these caves could also provide protection from the solar radiation astronauts would be exposed to on the surface of Mars. On the radiation inside a spaceship question...this is just guesswork, but yeah I think you'd be exposed to it even inside a spaceship. After all, it is constantly being bombarded by solar particles. Although the amount you're exposed to would be greatly reduced compared to that during a spacewalk for example, there's no way you're 100% protected.
Edit: Klaus' answer > mine.