I would imagine a tech would install an industry-standard cable from the truck; however, if you already have enough cable for the run, I'm sure a tech would use it and deduct the cost of the industry-standard cable from your charge...especially if the rest of the house is Quad.
The tech won't wait for you to go purchase it. Go buy it now and if the tech refuses to install, return it unopened.
I don't think a moderator would know the definite answer. I'd say it'd be up to the tech.
It will be ran likely with tri-shield. You will not see any noticeable degradation with tri-shield vs quad shield - especially if you're not right up against a cell tower or a neighbor who is a ham radio enthusiast.