Nats can come from outside but if your cage is inside it’s most likely to be overwatering of plants. To solve this switch the plants out of your cage for another one, place a mosquito tablet on the soil and water it in (harmless to animals and humans). If you don’t want to risk that vinegar...
The dome I bought separate from the light honestly not sure if it’s coil uvb or not, if you could drop a link or specific name I will definitely go shopping today😁