kemo,
The cinema plus connection kit is designed to have a wired connection from your router. The box basically converts your twisted pair wiring to DirecTV's coax setup. I don't think a "wireless" connection would work since all your HD receivers/DVRs register separately with your router.
Your options are to prewire a cat-5e line from your router to one of your tv locations (with a socket termination) or just hook the "Cinema Plus" connection (DECA) to your router with a short cord and run a RG6 coax to your splitter. Since your situation sounds like a new install, you have no way of knowing in advance where the splitter will be installed so you will have to let the installer do that. I did all the prewire on my installation since it involved some in-wall wiring that I wanted to do myself.
No one can really answer your last question. There have been many threads on this forum about what equipment installers have on their truck at the time they show up. While I do believe that they really try to have the proper equipment on their trucks, there are a lot of discussions about installers not having what it takes to do a complete install on the first try.
One thing I can assure you, if you do not have the "Cinema Connection Kit" on your installation work order it doesn't matter whether or not your installer has it on their truck: you will not get it installed. That is what happened to me and they wanted $75 to come back and install it. So, your real question should be whether or not it is on your work order. Then, if they don't have the equipment to install it on the first visit, they will come back and complete the job when they get the equipment.
(On edit, I see that stonecold answered one of your questions while I was typing mine. All good stuff.)