Hello.
Yes Diploma in health inspector is available in distance course, here basic eligibility criteria is to clear your class 10 or 12th with minimum aggregate 50% from any recognised board (depending upon the Institute) now your admission will be done on the basis of your score in class 10th or 12th some institutes take their own exam for admission so you may also face it, its fee vary from 8,000 to 30,000 per year depending upon the institute, exams in this depends upon the Institute either it may be semester wise or may be year wise.
Best of luck.