You can search for hotels by star ratings here: http://www.lowfareking.com/hotels/eur/england/london/by-stars/
There are no exact figures, because some of them are not registered ones. I can only give you an rough idea. There are 46,542 that have been registered into the hotels.
None. There is one with the name hotel but no longer let's the rooms.
A boutique hotel is a smaller hotel that is not part of a huge chain, but is still top quality. They tend to have individually styled rooms.
Yes