If the thermostat and UTH can get you the heat gradient you need, then you do not need to add any lights. How are you measuring temperatures inside the enclosure? Do you have a temperature gun? Or are you using an analog or digital thermometer?
How are you measuring humidity in the enclosure? Without knowing the exact humidity readings, we can't tell you if they're too high or too low.
As for guessing her age... that's hard to do without a photo and some measurements (length/weight). When you do take a photo, make sure you put an object in there for reference, like a pencil.
About her hiding... it's normal and healthy. Moving into a new home can be very stressful. Give her plenty of time to acclimate without handling her. Staying hidden is a normal snake behavior. Do not change the heat source just to try and get her out more. Let her settle in at least a week, then try feeding her. Once she is feeding for you regularly, you can start handling.
Congrats on your new scaly friend!