lounge. Flight crews (which include pilots and flight attendants) can be assigned to “airport reserve” which essentially means they wait at the airport in case they are needed. They would typically wait in the crew lounge. The FA they found in the crew lounge was likely just such a person. There are other reasons a crew member would be hanging out in the crew lounge.

Flight crews have various pay tiers. One is when they are actively working a flight. Another is when they are on reserve. It isn’t correct to say that FA’s only get paid when they are on the plane.

The “willing to fly” terminology could just be the gate agent trying to be funny to relieve some of the tension. Or it could be literal. Flight crews are assigned to flights in a variety of ways. More senior crew members essentially pick their trips. It could be a FA gave up a trip they wanted and had been assigned to in order to be assigned to your flight. There are any number of scenarios where “willing to” would be accurate.