UTH (at least the vast majority of them) are designed to go "UNDER THE TANK", not inside...this is for safety, they are not waterproof and you don't want a
shocking end to your snake, do you? Repti-carpet would not prevent spilled water from reaching the UTH (if UTH is actually in the tank). And yes, all UTH
must be regulated...most get too hot & snakes can get horribly & painfully burned from using them without regulation. Most only work (or work well) with a
thermostat also...they cost more but are more reliable. (some will work with manual adjustments using a rheostat but you have to be vigilant because the temps.
are less likely to stay dialed in) Heat rises...so yes, UTH belongs underneath....far less effective on the side, as the heat mostly rises next to enclosure & does
not go inside it. Thermostats can be used to control multiple enclosures but they'd need to be all the same size, for one thing, or the results would vary. And
I see from your list of species kept that they all need different temps...so that wouldn't work very well for you (using only one thermostat).