Ok... so here's the skinny:
The compact/coil bulbs are icky. And if it's a 40w, it's definitely one of those. I'm also a little concerned because I can't think of one that would put out much in the way of heat at all... Which makes me very concerned that it's not a UVB, but just a reptile basking bulb with UVA. At best the coil/compacts put out inconsistent UVB at worst they've caused eye problems and other health issues for beardies. But yeah, the entire issue could be lack of UVB related. Good UVB is another very important part of herp care. UVB emulates the sun with enables lizards to absorb calcium properly. And calcium does the same thing for reptiles that it does for people; makes strong bones!
All right you've got a couple options here.
Mercury Vapor Bulbs are the best. Easily. They produce heat & insane amounts of quality UVB. The two good ones are the Megaray (available at
http://www.reptileuv.com) or the T-Rex UV Active Heat (widely available, cheapest at
http://www.lllreptile.com.
They are $40 and last for a year. It's a screw in bulb- so while you do need a fairly large dome, it will work in one of those. They look like outdoor halogen lights. You could only use one of these if you decide to bump Indy up to the 125g.
The alternative is a flourescent tube bulb (like a fish tank). You want the reptisun 10.0. Again, it is significantly cheaper online, around $20 -compared to at least $40 in a store. A good flourescent tube is a perfectly adequate bulb. If this is a better option for you, do not feel remotely guilty in picking it! Tubes will not produce heat and need to be replaced every 6 months.
So- the tank.
This is sorta a hard decision. And it's up to you. Generally at the size you are talking about, I would say "go ahead and get your beardie in that larger tank". Because he's not eating and it might be related to stress/change... well... maybe keeping him in the 10 is a better option...
Personally, I'd probably order the Mercury Vapor Bulb (MVB) and put Indy in the larger tank as soon as that arrives. But I'm not there and I don't know your beardie...
If he seems to be having trouble getting his bugs in the larger tank, go ahead and feed him in the 10g.
Four crickets is not enough at all. When young, beardies can run through a ton of crickets. I mean upwards of 70 a day. Yes, I typed that right!
Keep offering the greens. He mostly needs protein while he's young anyways. They tend to surprise you by suddenly starting to eat their greens. Neither of mine took to greens right away.
And you need a new thermometer. The stick ons aren't efficient or particularly accurate. A good reptile store (or hardware store) should have a digital thermometer with a probe. The probe allows you to take the temp all over the cage. The probe does need to sit in a spot for a good half hour to get an accurate reading. Cold blooded animals rely on the heat we supply to get themselves warmed. Without that heat, their blood flows sluggishly and their organs can't function properly. It is crucial to good digestion. You want a hot spot btwn 100-110 and the cool side should be in the upper 70s or low 80s. This can be very very tricky to accomplish in a 10g.
Beardie
bathing is pretty common. My adults get baths (in my tub) once every 7-10 days. When they were younger it was more like a couple times a week. They do not appreciate these adventures... You might consider soaking him yourself in some lukewarm water (think baby temp) for about 20 minutes to help him absorb some water. My beardies won't drink water. I think Sinclair has 3 times in the 2 years I've had him and Pele even less than that. Some beardies do.
Take a fecal sample into the vet. It's always somewhat smelly- but if it's REALLY smelly, there could be a parasite.
Whew. Now that I just overloaded you with info, I'm gonna let you digest that! I think I covered everything important there....