1) doesn't matter if he's "half the size of the tank head to toe" , thats WAY to little room, what do you expect him to not move at all? bearded dragons need a 40 gallon at least after like 10/12 inches, hell my guy is only 8.5 inches and i would feel bad having him in a 20/30 gallon.
2) like i said, you need to get a new bulb, reptisun 10.0, its the most recommended/best bulb right now, it needs to give off good UVB so your dragon can be healthy(which he obviously is not)
3) whats wrong with sand? it can cause impaction, especially the calcium sand because they can't digest it. they can also grow to like the taste and just eat the sand as it is.
4) your basking problem only you can solve, i dont have your tank and what materials you have available to fix it for you. why don't you stop and think for a second and see what you can use to raise his basking area? go get a digi thermometer that has a probe on the end and take the temps.
5) you only need to add warmth if your room gets below 65 degrees at night, so if its does, yes get an OUT of tank pad and stick it on the side of the tank, not under and just at night.
6) feed him at least once a day, common greens are Collard Greens and Mustard Greens, can give them squash, blueberries etc. here's a list of the good and bad stuff for beardies, i have this favorited, i suggest you do the same.
http://www.beautifuldragons.503xtreme.com/Nutrition.html
also give him some worms like hornworms/silkworms/butter/waxworms from time to time.
there's also this helpful link up top that says
CARESHEET, i dont know if you thought about click that, it shows you how to CARE for a dragon. heres another link too in case you cant find it...
http://beardeddragoncaresheet.weebly.com/index.html
really hope that helps