I will be flying CX from HKG to Paris CDG (Terminal 2A) and have a separate booking on BA from CDG (Terminal 2C) to LHR. Terminals 2A and 2C appear to be within the same terminal complex. My transfer time is 1 hour 35 minutes.

I have two questions:

1. Can CX check my baggage through to my final destination with BA, even though the flights are on separate bookings?
2. Will I need to go through immigration at CDG? If I already have my onward boarding pass and CX agrees to check my bags through to my final destination (given that LHR is a non-Schengen destination), would I be able to transfer airside instead?

Any insight would be greatly appreciated. Thanks!