Hello to you ! I will try to answer your questions as much as I can
1. I don't really know hotels as I've always live near Paris. However, there are plenty of subways and trains and it's easy to travel inside Paris, so you don't have to choose only hotels in the center. It will be cheaper, as the extreme center of Paris is Eiffel Tower, Louvres Museum, etc, so it's quite expensive :p You can try to take a chamber near big train stations like Gare de Lyon, Chatelet les Halles, Gare du nord, Montparnass, or Gare de l'est, I know there are plenty of hotels here.
2. It really depends on what you want to do ! There are many things to do in Paris: we have beautiful parks, but also a looot of art museum, good restaurants, famous monuments ... Just tell us what you want to do and we can give you advices on it
3. It will be easier for you to travel in subways and trains if you know exactly where you're going, just to plan things. About subway prices, I highly recommand you, if you want to travel a lot in one day, to take an unlimited ticket for one day. It'll be cheaper than normal subway tickets. We can also help you to plan your trip if you tell us exactly where you're going
About food, I know some good places, depending on what you want to eat ?
4. Russians furs have always been so nice to me when I took the bus with them last year at ef ! I would have been happy to show you Paris if I wasn't already waited somewhere else this day
However I'll try to help you as much as I can, be sure of that :p Don't hesitate to ask questions !