Yeah, all I can say here is #1 he's never had any
UVB light, let alone a proper one, so he has severe MBD, and all the calcium and multivitamin dusting is completely pointless because he isn't absorbing a bit of calcium without a
uvb light. He needs 12-14 hours under a proper UVB tube EVERY SINGLE DAY, so unless you're taking him outside all day long, you need to get a Reptisun 10.0 (not a 5.0) immediately and get it mounted inside the tank, not on a mesh or glass lid.
#2, you don't seem to understand how important having a proper temperature gradient is to bearded dragons, they are not like other reptiles. You say you bought a "new heat bulb that keeps it nice and toasty", well that's not necessarily a good thing bud. You haven't even bought him a proper digital thermometer with a probe on it (no round gauge thermometers)...He needs a COOL SIDE between 75-80 degrees, a HOT SIDE between 88-93 degrees, and a BASKING SPOT between 100-105, and his basking spot must be within the correct distance from the UVB tube, unobstructed by anything, whenever you get around to getting one, which needs to be ASAP. If his jaw is cracking and popping the Metabolic Bone Disease (MBD) he has is very advanced, which makes sense since he's never had a
UVB light at all. His bone density is non-existent because he's never been able to absorb any Calcium because he's never had a UVB, so the "popping and crackling" from his jaw you're hearing is actually his bones and joints literally deteriorating. No joke.
And without proper temperature zones he cannot digest any nutrition at all. Bearded dragons bask under the sun (in captivity they bask under their UVB tube and their basking light) immediately after they eat, because in order to digest and process the food they just ate, they absolutely must absorb UVB and heat. You have absolutely no
UVB light, some kind of heat light, improper temperatures, and no way at all to even know if the new heat light you bought is literally cooking him. If his basking spot is hotter than 110 you're cooking him.
I'm not trying to be harsh here, but rather trying to get you to understand how sick this beaded dragon already is, and I'm sorry but at the very least he's going to have permanent problems, without a UVB tube and proper temperatures he's going to die. He'll become unable to use his legs, he'll start seizing and his spine will twist IP, and he'll die. That might be graphic but it's true. So please, take this more seriously and listen to us, we know what we're talking about, we see this every day, all day long. I think it's great that you want to help try and save him, but you need to act fast, because a year or more without any
UVB light kills most beardies.
And please, please, please, remove the pan of water!!!! He's either going to drown or he's going to be dead one morning because he fell asleep in it and the cold killed him. Please, no pans of water!!!! He doesn't need any water, they don't typically ever drink out of bowls, they get
hydration from their veggies and live bugs, and will usually drink if you drop water on their snouts with an eye dropper if you think he's dehydrated. But the pan of water needs to go now, he already fell asleep in it and I can't believe he didn't die, that happens all the time too.