1. Yes, B6 interlines with CX, so you will be able to check your bag at FLL to its CX destination.

2. I don't think that the timing is sensible. The flight actually arrives at 8:49 AM, 7 minutes later than you have posted (although I did not check every Wednesday in June). This means that you have 1:11 between brakes locked on the inbound and the push on the outbound. CX requires you to be at the gate no later than T-40. That is 9:20. This leaves you 31 minutes.

31 minutes is doable, but risky. Remember, presuming that the flight is on schedule, the brakes are locked at 8:49 AM. That doesn't mean you are off the aircraft and headed to Terminal 7.

All of this is premised on no delays. That is unreasonable for the heavily-congested NE airspace and for a short-haul arrival into JFK during the AM rush.

I would fly in the night before and overnight at one of the JFK hotels or fly in the day b efore and enjoy NYC. You can always drop your bags at the airport hotel, head into the City, enjoy yourself and head back out for the night if you don't want the AM rush.