With regards to your parents, I'm sure they know you'll want to be in a relationship at some point in your life.. and are aware about your need for privacy, particularly in the beginning of a courtship. I get you live under their roof but that should hold no restrictions about who you hang out with. There's nothing wrong with staying overnight at a friend's house.

Are you unable to stay the night because of your parents? Are you worried if you do, they'll ask you a hundred questions? If so, it's a boundary you'll need to set with them. Parents will always worry about their kids, even their grown kids. They don't get to pry, though, when that kid is in their 30s. I question the relationship you have with them and if they're hindering your development.

As for this guy, no, you don't need to tell your parents you have a boyfriend in order to sleep over at his house. He's looking at this from a selfish standpoint. He's closeted but in order for him to have you stay, YOU must put yourself out of your comfort zone and disclose a part of you you're not ready for. I don't like the double standard, coming from a closeted 60+ year old.