Yes it mostly covers the cooktop although it doesn't cover the control panel in front and it only hangs off the sides by a couple inches on either side. I don't use any supports on it although I probably should use some wood blocks to take a little weight off the unit. The glass of the top does get quite warm but its designed to take the heat. its the same material you find on a conventional smooth glass cooktop. I expect it gets hotter when you fry, the boiling liquid should keep the temp around 212F although the pot surface probably gets hotter.
You'll probably want to insulate your pot, that will help it boil faster. I used some bubble wrap with foil-looking backing, just 1/2" thick and it really helped.
Glad I could help, I'm new to induction cooking but I'm impressed so far.