We have a drop ceiling but rather large holes for the many light fixtures (at least 20, like a grid of light bulbs as decoration) in our basement. The holes are about 2 inches in diameter and the light bulb doesn't fill up the holes completely. Is it safe to live down here without removing the insulation?
Jeff answered the technically question quite clearly. As far as being able to live in the basement with the fiberglass insulation, yes you can. It won't shed any material unless it's disturbed. Ensure there is no moisture in the insulation as this would lead to further issues...mold ETC, but as long as it is in sound condition and not disturbed regularly it will be fine to live in the basement.
It's not clear from your description if you have recessed lights or not. Recessed lights can have an IC rating meaning you can put insulation right next to or over the recessed lights (IC stands for insulation contact). If the recessed lights aren't IC rated, then you have to leave a gap of 3 between the fixture and the insulation. Regardless of the above, you can always switch to compact fluorescent or LED bulbs which will generate far less heat for a given amount of light.
