The bulb in the 2nd pic is either a "basking" bulb, which is mainly for heat, or it could be a Mercury Vapor Bulb, which is the best type of bulb you can get.
As for your beardie, go get a large rubbermaid tub, by large, I mean at least 2 ft long, 1 ft across and 1.5 feet tall. Go to petco and get some stuff called "eco earth" or something similar. Prepare it per the instructions on the packaging. Put the product in the rubbermaid tub, about 10" deep or so. Insert your lizard, install lid. Check every 8 - 12 hrs. when your lizard is skinny again, put her back in her normal home. PM me, or re-post here and we can help you with the eggs. They can be fertile as Beardies can "store" sperm until the time is right. My female layed fertile eggs 8 months after being removed from the male! Hope this helps.
Bill