Here's a link for a White's Tree Frog care sheet. This should answer most of your questions about care:

Frog Forum - White's Tree Frog Care - Litoria caerulea

Turning the lamp off at night would be fine. You normally want to give your frog a 12 hours day/night cycle. As for the lamp, it really depends on several things. Most important is what type of light it is: LED, Fluorescent, compact fluorescent, incandescent, etc. And measuring light isn't just about the wattage of the light. Light bulbs emit a certain heat measured in kelvin, and I believe you want a light that's somewhere between 5700 and 6500k. I'm hoping others can chime in, because I'm no expert at lighting. Any more questions, just ask away.