two things you should get:
- a digital scale that can measure in grams, resolution 1 or 2 grams, max weight maybe 5 kilograms maybe 2 kilograms. available as kitchen scales. some come with a bowl that fits on top.
- a infrared temperature gun. there are different qualities here. search this forum for "temp gun". the advantage is that you get a decent temperature reading so quickly that its not a pain to check and re-check temperatures. regular thermometers or thermal couples have the disadvantage that it takes time to make a measurement.
1 month without food is no problem. sometimes they dont eat for several months. they still need access to fresh water, but on water alone, its crazy how long they can survive. but you need to make sure its not caused by problems with temperature, humidity, or some other husbandry-related issue. keeping track of the weight in grams helps to determine if its something serious.