Okay, first of all, no vet right now, that could literally be the end of him. As you already nailed, most available vets are "Exotics" Vets, who always seem to do more harm than good, and in just his past month on the forum, 2 young dragons who were perfectly healthy, eating, totally fine and just taken in to "Exotics" Vets for their first "Wellness Checkups" were quite literally killed directly by the Vets. So in this case with your little guy, he certainly cannot take any medications right now, that's not his problem anyway. His issues are husbandry issues, with the lighting, temps, housing together with another dragons, etc., and no Exotics Vet knows anything about husbandry anyway. So I'd hold-off on that right now.
A 10 gallon tank size-wise is fine, but the problem you're going to have, which is always a huge problem, is that it's impossible to get both a Basking Spot Surface Temperature between 105-110 degrees F and then a Cool Side Air/Ambient Temperature of no higher than 80 degrees, as the 10 gallon tanks are far too small to do this in. You're much better off to just go to Walmart and spend $10 on a 60 liter or larger plastic tube for him. They're cheaper and they work really well, and then you can just put your T8 UVB tube fixture right across the tube, no mesh lid to worry about.
***It's extremely important that such a young baby have a Basking Spot/Platform Surface Temperature that is hot enough for him so he can properly digest his live bugs, as once he starts getting adequate
UVB light he's going to start eating a ton of live insects every single day. Without a Basking Spot Surface Temperature that is between 105-110 degrees F he will not be able to digest his food, and babies can very easily become impacted due to this.
On the other hand, it is really equally-important that he ALWAYS has a Cool Side of the tank he can go to at ALL TIMES that is no higher than 80 degrees F at any time, this is crucial for him to be able to cool-down whenever he needs to. A 10-gallon tank makes this nearly impossible, the smallest glass tank that I've seen a proper Temperature Gradient be allowed by is a 20-gallon LONG tank (not a regular 20 gallon aquarium, you want it much longer than it is higher for a Dragon, especially if you are using only a T8 strength UVB tube that must be within at least 6" of his Basking Spot/Platform)...
As far as the Reptisun 10.0 T8 UVB tube, yes, if you're using a glass tank with a mesh lid, it absolutely must be strapped to the underside of the mesh lid, which can be done by simply using long zip ties, wire, twine, etc. and just putting it through the mesh and then just putting them around the entire tube fixture, and then just strapping the entire tube fixture to the underside of the mesh lid. Again, all T8 UVB tubes must be totally unobstructed, nothing at all between the actual UVB tube and your Dragon, and they must be within at least 6" of your Dragons's basking spot/platform in order to deliver adequate
UVB light to him...T8 UVB tubes also must be replaced once every 6 months, as they have a very fast
UVB light decay-rate, and at 6 months they are no longer emitting much, if any
UVB light.
****If you can afford it, you're much better off buying him a much stronger T5 strength UVB tube and fixture with a reflector inside it. Especially in his condition where he's already suffering from a Calcium Deficiency, he could really use the strong UVB and UVA light from a T5 UVB tube. You would also save money in the long-run, actually in the first 6 months, as the T5 UVB tubes only need to be replaced once every 12 months instead of every 6 months like the T8 tubes do. Remember, it doesn't matter how much calcium he eats, if he doesn't get enough adequate
UVB light every day he'll just excrete the calcium in his bowel movements.
The other factor you need to remember is that your goal with his lighting is replicating natural sunlight as closely as possible, and you accomplish this by putting an adequate UVB tube right alongside a bright-white colored Basking Bulb, both lights over the Hot Side of the tank, sharing the top of the Hot Side of the tank, with his main Basking Spot/Platform placed directly underneath both lights, so that he gets both lights at the same time while he basks. So you have to have both lights set up properly over the Hot Side of the tank only over his basking spot/platform, which must be the correct SURFACE temperature between 105-110.
*********BIG ISSUE: PLEASE DO NOT EVERY FEED HIM ANY SIZE OF SUPERWORMS, NOT EVEN THE MICRO SIZE!!!!!! He's way too small and way too weak right now to eat any size of Superworm!!!
Typically the rule is that you shouldn't feed a Bearded Dragon ANY Superworms at all before they are at least 12-14" long, some people even say 16-18" long. The reason is that they cannot properly digest them and their shells, and this may very well be the reason he's passing only urates and no fecal matter right now. Whenever young babies and juveniles (and I'm talking about healthy Dragons) are fed any Superworms and usually also mealworms, they almost always have bowel issues and become impacted...SO IF HE DOESN'T HAVE A BOWEL MOVEMENT SOON YOU NEED TO TRY A WARM
BATH FOR 10-15 MINUTES, AND IF THAT DOESN'T DO IT THEN YOU MAY WANT TO GIVE HIM A LITTLE LAXATIVE SLURRY, WHICH IS SIMPLY PRUNE BABY FOOD MIXED WITH A COUPLE SPOONFULS OF PLAIN, RAW, CANNED PUMPKIN AND SOME WATER.
Mealworms have no nutritional value to a Bearded Dragon at all, they are very low in protein, very high in fat, and pretty much all very hard, chitlin shell that Dragons cannot digest properly. So with your little tiny guy you just absolutely cannot feed him any mealworms, no dragons should be fed mealworms as a staple feeder insect (or even a treat in my own opinion), and superworms are a huge no-no!!!!
If you want to feed him an extremely healthy "worm", then you need to order some BSFL/Phoenix Worms, they are all soft-bodied so he can actually eat at least the size mediums (the smalls are completely pointless), probably the size larges, as I've fed only size larges to my month-old babies without problem. They are high in health protein that is non purine-based, unlike crickets and roaches, which is a good idea for him so he's not developing any Gout on top of the Calcium Deficiency, they are extremely low in fat, they contain a ton of water so they will keep him
hydrated, and best of all for him, they contain more natural calcium content than any other feeder insect (you still have to dust them, but they naturally have double the amount of calcium that other feeder insects do)...You'd probably have to order them as they are hard to find in pet shops, but I order mine from
www.dubiaroaches.com or from
www.symtonbsf.com and they are very cheap and quick shipping. I order 1,000 size large from the first place for about $25 shipped, so you could order 100-200 for very little. They would be the best live insect you could feed him...BUT PLEASE, NO SUPERWORMS AT ALL, NOR MEALWORMS!!!!!!
The pinhead crickets are fine for him, all insects that have a shell or a hard exoskeleton must be smaller than the space between his eyes. Sometimes very small babies get overwhelmed by crickets, so only give him 1 cricket at a time, see if he eats it, then give him another one. And always get any crickets that he doesn't eat right away out of his tank, as they do often bite them and cause infections...
As far as the liquid Calcium, the best kind you can order is called "Calcivet", it's exactly what a Certified Reptile Vet would give to you. Liquid calcium is much better absorbed by them as long as they are getting adequate
UVB light, but the issue with liquid calcium is that it's very easy to give them too much. I believe the Calcivet actually has a dosing schedule and amount.