Xiaoboa, wish we'd had talked first, as I could have saved you some money.
The Miracle Grow soil is prefertilized. Not a big deal, except it's more expensive than others due to that. Anyway, there should be no need for you to add additional fertilizer to the pot at all. Especially as the Miracle Grow fertilizer is already nitrogen rich.
(If you look at the package it will tell you the NKP relationship. There will be a three phase number---something like 12-5-5 or 10-10-10 or 15-7-5. In sequence that refers to the proportion of Nitrogen, Potasium, and Phosphorous.)
As to bottom watering. Put the pot in another dish (there are terra cotta trays made for this purpose, btw. Also plastic ones). Use some sort of shim to raise the plant pot a slight amount. Then pour your water into the bottom tray.
Whether from the top or bottom, overwatering is something to watch out for. Too much water is worse than too little.
There's no way of identifying pests or diseases without seeing the problem. Two recommendations, though. First, get some insecticidal soap (Safers is the one you most hear about, but there are other brands). Working outside, spray the plant with water, to dislodge as many pests as you can. Then spray with the soap, being sure to get the undersides of the leaves as well as the tops. Then bring the plant inside. You may have to repeat this because the spray doesn't immediately kill pests. It works by affecting them when they feed off the foliage.
As to the spots, there's no telling. They could be meaningless (being scar tissue from where critters have bitten the plant) to signs of a serious disease. Best bet is to take a couple of infected leaves to the nearest Extension Service office (there's one in most counties) and ask them to ID the problem and suggest remedies.
Lighting: By "cool white" we're talking about a normal, everyday flourescent bulb. You can get fixtures for them (and the bulbs) ranging from 18" to as much as 8 feet. The standard is four feet, and those holding two bulbs are often referred to as shop lights, because they're popular in workshops. But if you're just talking about one or two plants, an 18 inch "under cabinet" light will work just fine.
The designators (i.e., cool white, warm, grow, etc.) refer to how much of the full color spectrum the bulb provides. From your eye's point of view it doesn't matter---you'll see them as white light. From the plant's point of vew, however, the wavelengths that produce color may or may not be important. As I mentioned eairlier, for instance, fruit needs the red spectrum to ripen. Foliage, on the other hand, doesn't need anything on that end of the spectrum, but is happier with the blue/violets (which is what you find in the cool white bulbs).
Reason anything besides cool whites are so expensive is that they have to add specialized pigments to them in order to get the full spectrum. The normal powder used in flourescent bulbs doesn't have that stuff. So, both because the additional materials add cost, and there is more involved in the manufacturing process (and, sometimes, greed), the bulbs cost more. The full spectrum lights also burn out faster.
To put it in perspective, a four-foot full spectrum bulb can cost as much as $8, compared to a cool-white at about $1.29.
There is nothing wrong using the grow lights (other than cost). That is, there won't be a negative affect on the plant. You're just paying for something you don't need.
I'm concerned about directionality, however. The bulb you bought is designed to replace an incandescent bulb, and fits into that sort of socket. What sort of fixture are you using for the bulb you bought? Keep in mind that you want the light source kept only an inch or two higher than the plant, so either the light or the plant will have to be adjusted fairly regularly.
