Again, just to caveat my answers, I'm a newbie, so others please correct me if I guide wrong.
Hot plate, no. You want it warm and humid, not hot. The warming mat and thermostat that's made for germination has a probe that you push into one of the cubes that will regulate the temp. You want it just warm enough for condensation on the top of the humidity dome, but anything above 85, I think, would damage or kill the seedling.
Lights. I've read and been told that florescent are perfect for seedlings right up until they begin to vegetate. Next time I do this, I'll let them veg until about 3 weeks in (3-4 inches), I transplanted them after a week this time and it was too soon, too much stress. How many plants you want to grow will determine what wattage. A 400W MH or 600W HPS is good for a 4x4 foot area, which I have 9 plants growing well right now. I would think a 150W would be good for about 3 plants. I don't know about using CFLs for vegging, tho I see other posts on here with people doing that. A small cardboard grow box with a Flo tube or CFL and some ventilation and maybe a computer fan for when the seedlings get a little bigger should be all you need for a couple three weeks.
Feed and water in a pot. I'm doing strictly hydro with rockwool, so not sure how to work with soil and the nute requirements. I'm using Dutch Master Gold for my nutes and they have a good chart that's been working well for me on their web site.