Keeping humidity in a tank can be a real pain in the butt. I have a couple damp washcloths, a piece of plexiglass (which is a huge help with heat as well), and some towels if it's chilly in the house. On top of that, mist the tank and moss every day, a bowl of damp moss under the lamp (which seems to help it stay around 50% at least), and he has a humid hide with a tropical mix bedding that stays nice and damp in the middle of the tank.
Just a few ideas that I discovered through trial and error
You can get a thermostat for pretty cheap if you're on a budget, the herpstats are pretty up there. Mine is just an Inkbird Thermostat, around $30, and has been working just fine for me since last year. Just be sure to set the target temp a few degrees below 91, as it lets the temp get 2-3 degrees warmer than the target temp before it shuts off.
And exploring is great so long as he isn't constantly looking for a way out. I put my guy in his 40gal too early and he was ALL OVER the place until I planted it down, concealed the hides well, and even covered every side of the tank. At least make sure 3 sides are covered so he feels safe.

Feeding you may want to wait. If he's not settled in, chances are he won't want to eat and you run the risk of him not digesting properly if he's going to be squiggling all over the place.