How big is your snake? Your tank may be a bit too large if you've got a hatchling or jouvenile.
If your UTH is only taking your warm side temp up to 80 degrees, you should move your hide over there. I doubt your BP will ever really move to the cool side of the enclosure, and your BP needs a place to feel secure.
If your BP still doesn't use the hide, he/she may not like the hide. You need one that is just big enough for your BP to fit its entire body in plus a small amount of room to grow. Be sure there is only one entrance to the hide. Many BPs will not use a hide with more than one entrance.
Once you are sure your BP will use the hide, your next hide should be an identicle one on the opposite side of the tank.
A thermostat will be needed for your UTH. Get one ASAP. Your temps are too low and can result in a sick BP.
Feeding frozen/thawed food is easy if your snake will accept it. I'm lucky and have a snake that will eat anything. All I do is put my frozen food in a ziplock bag and sit it in a container of warm water until it is warm.
Make sure it is entirely thawed and push on the belly a little bit to see if there are any frozen spots left inside.
Next, I remove my hides and waterbowl too from the enclosure and and put in my thawed meal. I ust drop mine right in and Indy(my BP) goes right for it and eats no problem.
You however may have to use a paid of long tweezers to move it and trigger a feeding response.
thawed food you can leave in the cage over night, however I wouldn't recommend it. Leave it there for 15 - 20 minutes and take it back out if it is uneaten and stick it back in the freezer. I would only try to feed the same meal twice before you throw it away.
I hope this helps.