Welcome and no judgement from me. Lucky corns are very tolerant and forgiving. Corns were my first snake and I recently got one again because they are such cool snakes.
1. I can't speak on the thermostat mentioned but I will give you my take on it. Best bet would be to buy a proportional thermostat such as herpstat but these are a little pricey, but well worth their weight in gold. Next option which I have used for years on species more tolerant of temp fluctuations is a dimmer. Given your room stays within 5 or so degrees, this is an acceptable option for corn snakes.
2. The uth is plenty of heat as long as your room temps are dropping into the 60s for extended periods. As long as the little guy has access to a hide on a hot spot of around 85-90, he will thrive.
3. Aspen shavings are fine. When I used glass, I cut and glued ceramic tile to the bottom of the tanks. It helps disperse heat more gently and evenly. You can also put tile between the heat pad and table instead with similar results.
4. As long as the uth is regulated, I wouldn't worry about it. When I first started keeping snakes I used towels under my tanks with no problems. The bottom of the tank should have a gap for uth to fit. If it doesn't I would recommend the little sticky rubber feet you get at any hardware store. They look like a half bubble. Just big enough to allow the uth and cord from being crushed
5. Post pictures and welcome to the forum. Give us a little more info on your snake.