UK: pretty sure you dont get charged for anything execpt possibly ambulance/hospital if you are not from UK or EU, but I suspect it’s so unusual most NHS staff wouldn’t know how to bill you. Definitely no charge for sea rescue by the RNLI even though a typical shout for a Severn class ALB will burn £1-2k in diesel fuel.

Rescue insurance isn't hard to come by or particularly expensive for the group of people who spend a lot of time outdoors. The American Alpine club, for instance, offers rescue insurance with a membership, dollar amounts vary with membership "type."

I believe if it's a legit emergency, then no. If they find you obviously were clowning around, yes.

Most SAR teams are not dedicated to SAR, but do other tasks (firefighting, soldiering, etc) so SAR operations kinda fall under training.