They don't tend to like being near their poop and respond well to routine. My guy is trained to go outside of the tank too and it's very nice.
I had an issue with the ZooMed bulbs burning out frequently too. I switched to using a 90w PAR38 halogen flood light and they tend to be sturdier and last longer. That might be worth a try and you can pick them up at home depot most likely.
100w CHE is fairly powerful so double check the nighttime temps. You don't want the tank to go above about 75 most nights. I like to keep my tank between 70-73 (on a thermostat).
The Slimline t8 is a decent fixture for small tanks but I suggest upgrading to a 24'' T5 fixture. They are much more powerful and better suited to larger tanks. A T5 should sit about 12'' above the basking area.
http://www.lightyourreptiles.com/22-t-5-ho-fixture-high-output-with-arcadia-d3-12-ho-bulb/
For outside of the tank I suggest using a clamp lamp or dome fixture with a basking light (or MVB) hanging from an adjustable lamp stand. They will return to this light to bask and warm up when they're out and about. Either a PAR38 halogen or a 100w PowerSun MVB would be a good option for this.
The probe for the thermometer should be secured right to the basking surface to get the most accurate temps. It's good to have a second one on the cool side surface so you can see the gradient across the tank at a glance.