Keeping your pot in a sink of water is a great idea because, as you suggest, you can heat it or cool it easily by running hot or cold water into the sink. If the sink is large, compared to the pot, then you will have a lot of “thermal mass” in the water and it will keep its temperature for a longer time. If the volume of water is relatively small, then you will want to check the temperature more often and you might need adjustments more often.
I use two thermometers, one in the water and one in the milk/curd. The one in the water “predicts” the temperature that my milk/curds are headed toward. If you use one thermometer, be sure to clean it well as you move it from the water into the milk/curds.
You can “remove the pot from the water” only during the ripening stage (before you add rennet), or when you are cutting curds, stirring curds or cheddaring the curds. DO NOT move the pot at all after adding rennet and before you get your “clean break”.
One layer of cheesecloth in the colander is sufficient because you should have pretty firm curds by the time you drain them.
For a Farmhouse Cheddar, you typically won’t drain the curds overly long, so room temperature should be fine. Recipes vary, but some Farmhouse Cheddar recipes will have you return the drained curds to the warm pot for cheddariing and you’ll lose some additional whey then.