First off, you don't need to feed with ANY fertilizers until the seedling has four or more sets of leaves. Secondly, the tomato food you're using probably has a higher amount of Phosphorus to Nitrogen. Higher % N is what plants need in veg.

I'm not sure what kind of bulb you're using, but if it's an incandescent, get rid of it. Those put out too much heat for the amount of usable light they produce. Look into fluorescent fixtures, either tubes or CFLs. (Those squiggly looking bulbs that are about the same size as standard incandescent bulbs.)

You don't want a soil that holds moisture for too long, as this can lead to a fungal attack (a.k.a. Damping-off disease) that can kill seedlings almost instantly. If the soil you're using contains a lot of moisture retaining agents, you should consider adding perlite to the mix to help aerate the soil.

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