Signs of an upcoming shed are a pink belly and cloudy skin and eyes.

Spraying the cage down from time to time is fine. Just make sure it can dry out over a few days so mold doesn't grow. You should be measuring your humidity with a digital hygrometer so you don't have to guess when the humidity is low.

Spraying him with water won't keep him hydrated, providing freshwater and food once a week will.

Try to refrain from handling him for the next 7 days. I know he is cute but he needs to get comfortable with his new home and he can't do that if a huge monster is grabbing him all the time. After 7 days have pasted, try offering him a meal. Then wait 24-48 hours before handling him to allow for a digestion period.

Also, I agree with f4n70m. Get the accurite weather station to measure your temps. Its cheap and its the only thermometers/hygrometer you will need.