The chrysanthemum flowers probably didn't get pollinated, David and were probably also cut before they could start making seeds, so it's doubtful they will make seeds.
It is very likely too hot in the greenhouse for those cuttings, even in the shade under the table. That was what we call a "long shot" at best. If the leaves are looking dried out even in the greenhouse's humid conditions, they won't get any better in a dry condition even if it is cooler. Spray them with water whenever you get a chance.
Deadheading is cutting off the spent flowers when they no longer look pretty. As to the cross-pollination, I would think almost any zinnia can cross with any other. You just won't know what you're going to get.
