It's hard to say what time you will get on the road by as it can depend on how busy they are and how many changeovers they are dealing with. In the past we have contacted the local CA office direct and requested an early pick up time, one was no problem and the other wouldn't commit to it, so you could contact them. If you have no luck I would get there an hour or so early and you may get lucky. If your hotel is near to a store you could do a basic shop before heading to your RV depot as well. As it's your first ever RV trip, stopping earlier may remove some pressure and allow you to relax a bit more while you adjust to the driving style. However, there are RV parks a bit further on that would give you more time to adjust to the vehicle, there is a KOA in Kingman which is also a route 66 town where you could settle down and get yourself organised. Don't forget you need to make beds and stow stuff away etc as well. You could go further so it's a matter of how you feel about it.
You may think you will get to Page by Lunchtime but if you haven't already stopped along Desertview drive on the way out the east entrance you could easily spend half a day just admiring the views. There are also some native American stalls along the roadside selling their wares and the Cameron Trading post on US89 which has fascinating stores. You don't have to stop but just keep in mind that each journey between 'A' and 'B' will have lots of opportunities to discover new things.
After Tonopah there is an overnight rest area called 'Millers rest' (Google it) and is a pretty cool spot just to rest up. From Zion you could take the ET Highway and stop at the Little A'Lien Inn for a bite and to look at the 'Out of this world' alien photos.
The overnight temps will be dependent on the outside temps but you can have air vents etc open to help.