Is it okay to put gerinated seeds under lights?

I germinated my seeds until they had a tail, placed them in a cup with premoistened Light Warrior about a couple cm down, and put them under a fluorescent light that's about a foot above the plant. Should they be okay?

Yes. It will help keep the soil warm which helps the little girls grow roots plus once they sprout its good to have them under a light. Think about seeds that grow outside, they are under the sun for at least part of the day.

What type of light (watts, spectrum (cool white, warm white etc))?

Usually you want that type of light much closer to the plants (4" or so), but that depends on what your light setup is.

-spek