The round bottom leaves are called cotyledons and yes they usually die, it's all good as long as it doesn't spread but it doesn't look like it will. 3-4" away sounds good for your lights, I do 1.5-2" with them and have no problems. You distance the light mainly because of the heat the bulbs put out and yours won't get that hot unless the plant is touching it for a while. If you can keep the back of your hand there for a minute comfortably then it's ok for the plant to be that close.

Go to a local nursery or garden store and ask for some pesticide that's safe for fruits and vegetables, should only be a few $$$.