Sorry; was out all day.
Yep, chicken goes into a pan all by its lonesome. Pan should be preheated. If you're using a conventional rather than nonstick pan, the chicken will release from the pan when it's cooked. Anything which sticks will served as the basis for your sauce, as you later add liquid and scrape up the goodies in the pan. Adding the liquids first would be more inclined to hinder the browning process and would likely add more of a poached character to the chicken depending upon the heat used and the amount of chicken in the pan.
As for the mushrooms, this is going to depend again upon the heat and the pan used. It appears that Cheryl did the mushrooms in a dry pan, which could be done if you control the heat carefully, as mushrooms will exude their own moisture when cooked. If I were using this recipe, I'd likely try it that way and if I'm not satisfied with the way they're cooking, I'd likely add a small bit of the marsala to jump-start the cooking process a little.
It's kind of interesting to note that the two chicken marsala recipes on the forum are cooked in opposite order: one starts with the chicken, the other starts with the veggies. Apparently, both of them seem to work out pretty well for the people who tried them! 