The temperature is measured in degrees Celsius. Celsius is the name of (one of ) the scales to measure temperature, not a measurement unit. The measurement unit is the ”degree Celsius”
Agree. It would sound better as "the measurement is in degrees Celsius" in my opinion.
Does the word gradul really mean degree or graduation. A full translation to spoken English would be the graduation is in degrees celsius or in celsius or in centigrade more often in the vernacular... or the scale is in centigrade or similar
"gradul" refers strictly to "the degree". If you refer to the graduation (marking on a container indicating a measurement) that would be "gradarea" (marcarea diviziunilor pe o scară de măsură a unui instrument)