My thoughts:
1. Do I use a heat mat, heat lamp, or BOTH?
One or the other. Most people choose a heat mat but they must be regulated with a thermostat otherwise they get way too hot for a Corn. You need the floor surface in the mid-80s on the warm side of the tank, which will feel barely warm to you - you'll be surprised how cool Corns need it.
If you go for a heat lamp insted, that will still need a thermostat and you need to buy the right thermostat for whichever you choose. Many thermostats are designed only to be used with a mat and won't work properly with a lamp. Ideally you need to run the setup without the snake for a few days, to tweak the temperature and make sure it's right.
2. Do I leave these heating devices on ALL day and ALL night?
Yes. As you'll be controlling the heat source with a thermostat, this will automatically turn it on/off in order to maintain a constant temperature. You don't need a difference between day and night.
3. Do I NEED thermostat or is a thermometer just fine?
You need both as they're different bits of equipment. The thermostat controls your heat source and the thermometer measures the temperature to make sure it's OK. Thermostats behave slightly differently depending on the make/model of your heat source so you need the thermometer to check it. You need a digital or infra-red thermometer as the plastic dial or cardboard strip types can be 20 degrees wrong either way - enough to kill a Corn. The critical temperature is where the Corn will be able to get in contact with the hottest surface. With a mat, this will be the floor surface immediately above the mat. Don't bother measuring air temperatures in the tank, as the Corn won't be up there.
4. Is it okay to feed a baby corn one pinky mouse a week?
It's more usual to feed a pinky once every 4-5 days as a hatchling. As they grow and the food size increases, you feed them less often. My adults eat one large mouse every 2-3 weeks.
5. Does aspen substrate cause mites? (the packaged zoo med kind)
No. They would very soon lose customers if their substrate carried mites. Reptile mites are caught from other reptiles but they can be transferred by people, equipment etc.
6. IS tap water okay for snake to drink and soak in?
Yes.
7. How long do I have to wait until I can handle my snake after buying it?
We usually recommend leaving it completely alone without handling or feeding for a full week, apart from water changes or spot cleaning. This gives it a chance to get used to the sights and smells of its new home.
Hope that helps. Welcome to the most addictive hobby in the world!