I = me/other typical escort
Q: What exactly is an "overnight" session?
A: We meet at some point in the evening, usually have dinner and then it's off to the races. I spend the night and then in the morning after some interaction we shed tears and bid our fond farewells until next time.
Q: We'll spend the entire night doing... what?
A: It won't be having sex, if that's what you're asking. You wouldn't want that, and I can't do that (and most escorts can't either), so imagine having a guest over for 12 hours and what you might do to fill the time.
Q: I'm currently in touch with this guy who I want to hire, and he suggested the "overnight" option...
A: Imagine 12 hours of fun with a friend, because you guys know things about each other, share things in common, communicate well, and so on. Now imagine 12 hours of awkward silence punctuated with brief bursts of single-word answers to your questions, followed by however long you'll be filled with regret for paying for that 12 hours. Now imagine talking on the phone for 15-30 minutes getting to know someone to see if A or B is more likely (which should have already given you insight into how your first question should be answered).
Q: Are we suppose to have some fun but he will eventually expect some "off time" to get some rest?!
A: It depends on how you define "off time." When I did an overnight with a client, the only off-time I had was being asleep because I was a guest. A guest for 12 hours doesn't get "off-time," and I didn't want off-time. I agreed to do an overnight because they seemed fun. If you're defining "off-time" as a break from a particular activity, that doesn't mean your escort should go trot his ass into another room to answer emails or phone calls or have some "me" time. You guys can talk, laugh, eat something, watch tv, etc.
Q: ...say 11 pm
A: This is too late in the evening to get started for an overnight.
Q: ...say 11 pm, and we will spend the entire night doing what "I want" or rather "what I hired him to do"
A: In my opinion, you don't want an overnight as much as you want an extended late-night session for 3-4 hours. If an escort is trying to convince you to hire them for an overnight that starts at 11pm, here's what will happen.
11:30 pm
You: Well that was amazing!
Escort: Yes, it was. I'm sleepy. Good night!
There are a gazillion threads on this forum and just as many opinions on what an overnight is, and what an overnight should be. IMHO, sex is one component but not the only one. You'd be amazed at how quickly you can get bored with someone you don't know in less than 90 minutes.