Don't even turn your UTH on! Just leave it off until you get your thermostat in. Your snake will be okay. If you turn it on, it will heat up all the way (sometimes to 130*+ which will burn your snake quickly)
Yes, the thermostat will come with a probe and that's what you place between the UTH and the glass. Basically what it will do is only allow x-amount of power to the UTH so it doesn't heat up all the way. It's not like an on-off type of thermostat where it turns on full blast until it gets to 2*ish above your desired temp and then shuts off until about 2* below your desired temp (the hydrofarm works like this). Your UTH is on all the time but it's only heating up enough to reach your desired temp. That way, there are very little fluctuations in your temp.
When you get your thermostat, you will plug the actual unit into the wall and plug the UTH into the unit. Then hook up the probe and configure the settings. Then it's good to go!
As for the power strip, I have one of those that I used for a little bit. Honestly, it's not worth it. If you need the CHE for extra heat, chances are you need that extra heat all the time. Since your ball python doesn't need a day/night cycle, it's not necessary. now, if you had a corn snake, I'd recommend one of those with a day and night bulb. But you don't need it for ball pythons.