It's good news that she ate a bit. Don't force it, but let her take what she wants. A couple teaspoons is pretty good. It's better to offer less at once multiple times over the course of a day than a ton all at once. You want to ease her system back into shape rather than shocking it with a ton of good food all at once.
As for the bulb, given her condition I wouldn't trust it aside from using it for heat if it's putting out the proper surface temperatures. I can give you links to good UVB setups if you'd like. The T5 setups generally cost between about $50-100 including a good fixture but the fixtures will last years and the bulbs will last at least a year before needing replacement. The high quality output is well worth the investment.
As for the bulb, given her condition I wouldn't trust it aside from using it for heat if it's putting out the proper surface temperatures. I can give you links to good UVB setups if you'd like. The T5 setups generally cost between about $50-100 including a good fixture but the fixtures will last years and the bulbs will last at least a year before needing replacement. The high quality output is well worth the investment.