Ice water is not a substitute for a proper ice bath. You need more ice than water and you must stir it. The melting point of ice is reliably 32.0 F, but ice water is just chilled water.
Mash temperature is tough, because the mixture is kind of chunky and the temperature will vary throughout. The actual sensor is pretty tiny in that tube on a digital thermometer. Its about the size of a pencil tip. Its a no-no to stir with a thermometer, but if you could attach your probe to something like a wooden spoon and stir, that would give you a good average.
I use a certified analog lab type thermometer and the bigger volume on the tip does a good job. Digitals freak out around induction plates.
I set my strike temperature and dont even worry about mash temp. Every so often I round up my thermometers and measure the strike temperature. If they agree, Im good.
Cheap oven thermometers are bad about getting water in the cable. If you get the cable wet it can give you some wacky readings. You can dry it out in the oven but eventually it will corrode inside. If the cable gets stiff anywhere along its length, toss it.
Dont worry about boil temps, boiling is boiling. Also wort boils a little higher than 212F. Anything dissolved in water will raise the boiling point. Dont panic and assume your thermometer is wrong.
