Ok,
I'm serious, REMOVE the heat rock. See if you can get your money back or whatever but GET IT OUT of the enclosure.
Don't get another hide, your lack of reliable stable heat is your biggest problem and it is a BIG problem, the biggest in fact.
the UTH is going to get way too hot if its just plugged into the wall. Don't use it until you can control the output. Do this with a thermoSTAT, NOT a timer.
I guess you should put the temp strip on the substrate to get the best reading but even an analog thermometer would be an upgrade but ultimately you will want a digital or even better, an IR. Use this to try to get mid to high 80s in the tank with the lamp.
And READ, you said you know the basic stuff, I'm not sure what you meant because this is the basic stuff.