"Do they sit at home with a pen and paper and think?"
Basically, but reading papers that are being published each day is also a huge part of the work involved.
"Are they focused more on academics or research?"
There are institutions where physicists can just focus on their research without having to burden themselves with teaching at a university and all the tasks that come with the professor position. So basically, some of the most gifted physicists are able to focus on research, but most have teaching responsibilities.
"Do they work in teams or do they work alone?"
Some work alone, especially if they are pursuing a very unpopular approach to the problem they are trying to solve. But groups are more common.