Actually I don't think it's a proper mall in the American sense and I didn't go inside to check it out - maybe someone else on the thread can comment on it if they went in. I think it's more of a big Convention Center with a 'mall' of restaurants, a movie theater, and some shops (like the Gap).

Yes you can definitely work in your room there's a comfortable desk area and the view of the Eiffel Tower is stunning

There are even places to work in the lobby (though it can be crowded) - a restaurant in the lobby too where you could work. I've been working from the Exec lounge mostly (so if you can get access to that, it's worth it).

You definitely won't starve! When you want to take a break just walk outside the hotel, turn right and walk up the street and you'll see it's lined with all kinds of restaurants, bars, cafe's, etc.