Depending on the type of heat tape yes, ambient temps will be a BIG problem. Heat tape does basically nothing to raise the cold side temperature. So you will be risking either RIs because of the low temps or your snakes never wanting to leave the tape because its to cold everywhere else, so now you are only providing 4"x16" or so of useful space. I keep my racks in a dedicated reptile room with separate ambient heating from the rest of my house. A lot of people here do the same. Its the tradeoff with the space efficiency of racks
That being said I did see an interesting rack design at the last reptile show that was built with this issue specifically in mind. It used much larger heat tape then the usual 4" (I think it was 12"? Not 100%). It also had a slot where you could add additional 4" tape to the cool side yourself and run it on a separate thermostat to control your cool side. Unfortunately I am completely blanking on the dude's name, all I can remember is that he won a reptile report award for his racks.
Yes, you can raise babies in adult sized tubs. I am currently doing it with several juvenile BPs in V70 tubs without any issues
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