Diy background is totally what i have been wanting to do on at least one of my future tanks. I would use super glue gel though as silicone tends to not hold well... and yes this makes your background permanent on that tank lol.
As for hiding the heater effectively, you would probably have to sacrifice a lot of space to place a tiny powerhead in the back chamber to circulate the water around the heater and out. the water would have to enter one disguised opening in the background and exit another disguised opening. at least thats how i envision it.
@Thyra:
Activated charcoal/carbon to my knowledge does not remove nitrates. it can adsorb ammonia and i think nitrites directly, thus preventing the formation of some of the nitrates, but 1. it sort of competes with the nitrifying bacteria in your tank and 2. it adsorbs things fairly fast if there is a lot of ammonia getting produced at once by an overloaded tank or something like that, so it becomes useless quickly in that case. This is for FW. for SW carbon is mostly used to take out other impurities out of the water like toxins from fish, and invertebrates, and w/e other dissolved pollutants in the water (often things that cloud the water)
As far as I know the vodka dosing is used in SW only. its something like creating a population of bacteria that feed on phosphate or nitrate...or something that feeds on w/e food algae normally feeds on, thus effectively out-competing all algae in the tank, leaving the tank very clean of algae and free of nitrates and possibly also phosphates, but im not sure as i dont remember much.
@ ryan: You can also put the heater either next to the filter intake or filter output to get water flow past it....