My encounters have all been with Indys, so I don't have extensive knowledge of agencies, but would imagine that things are similar in many ways, the Indys just do their own booking.
When the clock starts varies by lady. If I am late for whatever reason, I presume that time has evaporated unless she says otherwise. I always communicate my estimated arrival, usually through text. On appointment day, I send a text in the morning confirming the appointment, send a text 20-30 minutes before letting her know I am on the way, and then another when I arrive to see if she is ready.
I do mostly hour or 90 minute appointments. With my regulars, they usually run long. With one lady, I usually plan on 2-3 hours (she likes to talk, and we usually eat). With another 1.5 - 2 hours. My ATF is so generous with time that I actually increased what I was paying her because we never parted at the hour. On first visits, I presume we are going for exactly the hour that I scheduled. If she is running late, I believe the clock starts when I walk through the door. I also believe it involves shower time. I try to be within 5 minutes of the hour in departing, unless the lady offers for things to run longer. I have had a couple of ladies that wanted some 'get to know you' chat before things started. They always told me not to worry about the clock. One asked 'how long can I keep you today?' If nothing is indicated otherwise, I will move from chit chat to action after about 5-10 minutes to make sure we finish on time.
As for menus, I get an idea from websites and/or reviews. After an initial meeting, I am not bashful about just asking the lady if she would enjoy doing XYZ. They get requests for all kinds of shit far stranger than anything I ask for, so I've learned to make the requests. Have one friend that likes to be submissive. I have taken to giving her exact instructions on how to dress and act when I arrive - it's led to some fun role play.
I stay away from backpage. There are some ladies that I see that advertise there, but they are also on other sites. Have a strong preference for ladies on P411. Have never had a bad experience with P411 ladies. Mostly use ECCIE for reviews, sometimes TER.
TL;DR. Be polite, follow rules. If you click, the rules will bend to your favor. Be timely, arriving and departing. If bonus play is offered, I always accept with a great big smile.