Humidity in a rack comes partially from the room and the rest substrate and water bowl size and location.

A herpstat 1 is a great choice as long as you room is not cooler than 75º if that is the case you may need a HS2 or HS4 because a single heat source may not be enough.

Yes the herpstat one, two, and four will with the addition of a humidity probe HOWEVER a herpstat one only has a single probe so it can, but it cannot control a heat source at the same time.

A 32qt tub rack will work for adult, sub adults very large females may require larger.

Heat tape is as safe as the installer. It often requires electrical installation so the competency of that effects the safety. The second thing is I do not believe a heat source should be able to max out past 100ºF. Some heat tapes will exceed this others do not. Same holds true for UTHs.

IMO no a rack is not the best option. It saves a huge amount of space. It is harder to heat than a well designed custom enclosure, humidity is about the same, and I find them far harder to clean. (twice the surfaces to clean wash disinfect in a smaller space.)