This is a fairly easy Square to circle if they can hand things over temporarily to a compliant holding company until Brexit.

Another reason why we need to get out TBH.

What happens to customers who have bought flight with TC? Will Fosun honour these bookings or will customers lose out?

As it is an ATOL protected booking TC would have to provide a replacement flight.

Its a flight only booking (not a package holiday) and doesn't have an ATOL certificate or reference on the confirmation so I assume its not covered under ATOL.
Will FOSUN likely honour existing bookings or are they more inclined to cancel them and customers lose out.

Selling Thomas Cook to Fosun without its airline will be like buying a sandwich with no filling in it. The success and past profitability of TC has been its vertical integration of the TC tour operator with its airline and its travel agency. Just ask the top 2 package holiday operators in the UK - TUI and Jet2. Over two thirds of holidays sold by TC are using its own airline and they are sold as a package. If TC sells the airline, then it potentially ends up having to buy seats elsewhere at a premium mark up from its arch rivals (TUI, Jet2, Virgin, Lufthansa, EasyJet).