T8's at 4" should be fine. But if you are uncomfortable with it, there is no penalty for backing it up to 6 or 8 " for a while to see how things progress. At the cotyledon stage where you're currently at, it doesn't matter much. The cotyledons are basically giving the plant what it needs to get through to true leaves, and would probably do so in the dark. Cotylendons are not just photoreceptors like true leaves and may not be photoreceptors at all (I'm not sure); they are primarily little nutrition storage depots. Like the booster rockets that get a rocket off the pad and into space and then fall off - just as the cotyledons will do when their work is done. So light is something you don't need to sweat right now. Eventually, after there's a couple sets of leaves, you want to get it down to as close as you can go without the leaves being hot, which is usually about 4-6" depending on the lights. It's pretty variable. My T5's will turn most plants purple at 8 inches and need to be backed off to 10 " to prevent purpling. However, there is no real penalty for leaves turning purple - the plants, strangely, don't seem to care and grow fine regardless.
You'd have to post a pic to get an assessment of whether there's something going on with bacteria or fungus, but there probably isn't anything wrong. Green always looks yellower than it should, especially when the eventual pepper is particularly desired and unavailable in the supermarket.
+1 on bottom watering.
-1,000,000 on using a spray bottle. Don't water with a spray. I did that on one tray of 8 and they all died together, overnight, after about 2 weeks. Just died of thirst. The spray deposits a tiny amount of water on the surface, where it's almost immediately evaporated off under the lights. Spritzing water onto the pots never makes it to the roots! Either bottom water (best), or carefully water in from the top with a pitcher with a narrow snout or small-diameter neck around the sides of the pots so as not to disturb the delicate seedlings. Put in enough water so it really gets to the bottom, and then relax for a week.