London + Paris 12 days itinerary

19/12 evening HK to London by BA
20/12 arrives Heathrow in early morning, go to Saturday flee market and sightseeing (London eye, Tower bridge, London bridge, etc.)
21/12 go to Windsor for a whole day
22/12 get into Eurostar and go to Paris, sightseeing in Paris (e.g. Louvre)
23/12 visit Versailles, museums, etc., have dinner in a Michelin restaurant
24/12 go to Fontainebleau for a whole day, then go to watch Moulin Rouge at night (11:00 show)
25/12 visit Eiffel and Seine
26/12 go to Mont. St. Michel for a whole day
27/12 go to shopping and then go back to London by Eurostar in the evening
28/12 go to Greenwich and shopping (crazy sale) and sightseeing
29/12 go to Cambridge and then back to London on the same day
30/12 Buckingham, Westminster, big Ben, Downing Street, etc., and watch the Opera in the evening.
31/12 ultimate shopping in London and then leave London at Heathrow in the evening (18:00).
01/12 arrives HK in the afternoon.

Questions:

1: Would it be too tight / hurry?
2: Is it possible (& good) to go to Bath?
3: Is there a new shopping in London just opened? What is it? Where?
4: Is it safe in the district of Moulin Rouge? Would it be ok (safe) when I leave that District after watching Moulin Rouge (around 01:00am)?
5: What transportation can I take after watching Moulin Rouge (around 01:00am) on 24/12 (actually, it should be 25/12 01:00)? Is it easy to get a taxi at there at that time?
6: Any other comments on my itinerary?


Thanks