Ok firstly calm down and get some proper sleep
Snakes are not made of glass, a few fluctuatons here and there are not going to matter.
Which answers Question 2, an ambiant temp is the middle of the viv. Your cold side temp is fine at 27C, in fact 25C would be better but it's not that important so long as the snake can thermoregulate and there is a gradient from one side to the other.
As far as sticking things down to plastic - some probes come with a little suction cup attached to them and they work well on plastic walls.
You can stick it down with a blob of aquarium sealant which will peel off when you're finished with it.
I've seem people drill/melt 2 littel holes in the sides and put a cable tie through them to then tie the wires to
or simply just run it down the wall and along the floor and put something heavy over it to hold it to the floor, edge of a hide will do this.
You thermometer probe needs to be on top of the substrate - not underneath. You should always measure your hot spot where the snake will be sitting to get it's heat from.
The thermostat probe is fine under the substrate or you can stick it to the outside of the tub a few mm above the mat.
They can move things around so maybe stick it to the wall pointing down over the mat so it just touched the floor with some sealant will prevent it being moved.