It shouldn't cost anything, but you may not get it. We were able to get a late check-out last month (12:30pm instead of 11am) just by calling the night before.
What time are you thinking of? I know in the past you could call mousekeeping and ask and sometimes they would let you do it, and 1:00 has been the latest they would ever give out.
They are. We got late check-out at YC in mid-June. OP, it doesn't cost anything if they are able to grant your request. The latest we've ever gotten is 1:00 pm. The best thing to do is go to the front desk the night before you check-out and request late checkout. The CM will then check to see if the request can be granted.
We usually just book an extra night if we need the room for a late flight, then there’s not a need to depend on a last minute answer from housekeeping. We tried the “just hangout by the pool” thing once but it rained and we felt like we dn have a place to go so I didn’t like that.