Question about ajwain (Carum ajowan) | Vegetable gardening | Commercial Hydroponics farming

Hello, I am from near Naples in Southern Italy. I am not Indian but as I am interested about your wonderful culture, sometimes I visit the ethnic stores in the city to see what they have on sale. In one I found ajwain seeds, and as I like their taste I tried to plant them, with success I have to say - most seeds sprouted and so I have many plants on my hands. Most also seem to be growing well.

The question I have is regarding the leaves and the stem of the plant: are they edible? I have not been able to find any conclusive answer - by the way, I have also noticed that in southern India the plant that many people seem to refer to as ajwain is actually a different plant, the one called Cuban oregano elsewhere.
While in northern India ajwain refers to the plant I am talking about, the one which looks somewhat like parsley and celery as they are part of the same family.

Thank you for your interesting website, too.