That would depend on the frequency that the solar panel accepts and the frequency of light that your lamp gives out. It may or may not work. The sun gives out a much broader spectrum of light, which is why solar panels are much more effective in sunlight. I have seen solar panels charged by lamps, but it usually doesn't work that well and I have never seen it work with fluorescent lighting.
Sure!...did you ever use a solar powered calculator indoors under a lamp?? It works just fine.
yes, although charged is the wrong term. But for every 00 watts you put into the lamps, you will get well less than 0 watts out of the solar array. Well less. .