Yes, all my coworkers, including my managers are now younger than me. So when a manager takes everyone out, the waiters assume that I’m the one treating everyone to lunch.
Yes, I've had that a few times. Although being substantially older than your manager is externally no big deal unless you make it so, in the cold dark recesses of your own mind it can really start to grind some gears if you let it.
That first happened to me at 18 and it was so weird. I was helping out at my old school for an interschool music festival—a week of all sorts of different workshops and rehearsals between different schools, culminating in a concert at the end. During a break I was tinkering around on the piano, and a student came up to me and said "excuse me, sir…[some question about the timetable or something, that I definitely didn't have the level of authority to know the answer to]". I have her the best answer I could and she went on her way, but I was just stuck there feeling way too old.