Hiya just a few answers, you should upgrade to a 4ft tank atleast
but at 12 inches I'd doubt he was an adult just to let you know unless he has severe stunted growth.
You should let the vivarium air out because the fumes of bleach may cause issues.
Offer quite a shallow waterdish at all times filled with bottled or water thats been treated and bath every day if you like for 15 or so minutes in lukewarm-warm water not too hot at all you can bath not as often but bathing is a primary source of hydration.
The sand may be an issue as they sometimes eat quite alot of it when messing around and it can cause impactions but some people succesfully use it. I use slate tile from B+Q and I don't need to cut mines nails as it wears them down when he's running about.
Your temps should be ok, but your better off with it just over 100 than just over in my opinion 110+F for an adult is a no-no in my books though.
Heatmats shouldn't be used as beardies detect heat from above using their "third eye" so you may want to get a higher basking bulb I find a drop to room temperature at night to be no problem myself.
Don't feed food from outside a guy I know of had his beardie who died. Ater eating native grasshoppers and becoming hooked on them, he was unable to keep them breeding and was forced to hand feed and he refused until the point where they had him put down.
Dusting with nutrobol is fine but do it twice a week and use a pure calcium every other time, I don't use powder on my veg as he won't eat it with powder.
Your better off just taking your beardie out in the summer than letting him in a run I suppose you could setup a small one but always keep an eye on them because they WILL try to eat bees and wasps! In asda they sell mixed salads from 50p-£1 I use those for my beardie they normally have escarole, endive etc in them just check the back. I offer greens every other day or unless he has finished them give insects around 3 times a week if hes actually an adult but at 12" I'm not sure.
that's a great forum to join up with!
hope this all helps a little, feel free to send me a Private Message any time for help.