I'm playing around itineraries to allow a couple of days in Havana before the embargo is lifted and some quality diving at Bloody Bay wall in the Caymans. Routing home the easiest option on a Sunday seems to be an Air Jamaica flight from HAV to KIN giving a reasonably comfortable 4 hour window for the BA flight back home. A couple of questions building on the information above:

1 What time does BA check in open?
2 Is there anywhere to dump bags at the airport if the answer to 1 is 2.5 hours.
3 Anywhere worthwhile to head for a snack near the airport
4 Am I pushing it with a 4 hour connecion?

Thanks