1) Specification and Size:
a.Front panel size75(L)×34.5(W)mm;
2) I had a friend use a reptile heating pad, once, taped to the carboy. He said he wouldnt do it again.
3) That depends on whether you want precise temp control or just a variable temperature range. I, personally, dont care about precision in my temp controls as long as the temperature sticker is in the 60's for my ales.
Others, tend to want precise temp measurements. Be careful about dropping your thermistor into your wort, I have heard that they can be damaged or at least disrupted if they aren't water-tight but I have not had that happen. Like I said before, I bought a $0.98 aquarium thermometer that I stuck to the carboy and use that to adjust my STC-1000. I have found that I have to set my STC to around 62 at its lowest to get my active fermentation temp around 68
Yeast: those exothermic bastards.