It's good he's responding to the water! Careful not to give him too much at once. Little bits at a time will do well enough. That's the first step so good so far!
I do think a solid substrate like non adhesive shelf liner would be better because it's easy to keep sanitized. Even paper towel or butcher paper will work for now. If you want something softer, try some fleece perhaps. That can easily go in the wash if it gets dirty.
I don't think the previous owner was giving proper care given his condition. He is showing signs of malnutrition and improper exposure to lighting. The
UVB light should probably be replaced right off the bat. I'd pick up a T5
UVB light like this one:
http://www.lightyourreptiles.com/22-t-5-ho-fixture-high-output-with-arcadia-d3-12-ho-bulb/ That is what I use and it is excellent. It will also last for quite a long time (over a year with good output). It should sit about 12'' above his basking area (overhead over the hot side of the tank).
It's also important to get accurate temperature readings. I suggest using either a digital thermometer with a probe for each end of the tank, or an IR temp gun so you can get instant readings. Something like this will do nicely
https://www.amazon.com/Nubee-Temperature-Non-contact-Infrared-Thermometer/dp/B00CVHIJDK You may be able to get something similar in a local store. You want to adjust the height of the basking bulb so it provides an area of around 100-105 in an area at least the diameter of his length nose to tail. Some areas of 90s around that and a gradient down to about 80 on the cool side. An adjustable lamp stand is helpful for this.
Overnight, I wouldn't use a red bulb because that's visible and can disrupt his sleep. Normally they don't need overnight heat if the temps in the tank stay above about 65 but in his case his system needs some support so keeping it around 75-80 is a good idea. You can use a ceramic heat emitter or a heat projector
http://www.reptileuv.com/shop/index.php?main_page=product_info&products_id=196 to do this. Just adjust the height of the bulb to provide the correct temps.
If he can be handled, he may enjoy some time outside in the natural sun on your lap until a new
UVB light arrives. This may be too stressful though so I'd do this only if he seems like he has the energy. You may need to wait until he bounces back a bit before it's doable. I'd try to get the
UVB light in as quickly as you can as the
UVB light and proper heat are critical for his health.
His care is going to take quite a bit more work than normal, but it's absolutely worth it. Several of us have helped dragons recover from pretty serious conditions and are glad to help you along the way with advise and experience. Please keep us up to date on his condition.