D.Pharma

Yes, Diploma in pharmacy can be pursued via distance education. Yes, you can get a license to open a medical shop, however there are a few pre-requisites that you have to fulfill, which are mentioned below:
Requirement for obtaining Drug License
The following are minimum requirements for obtaining drug license or starting a pharmacy in India:
Area: The minimum area of 10 square meter is required to start a medical shop or pharmacy or wholesale outlet. In case, the pharmacy business combines retail and wholesale, a minimum of 15 square meter is required. Storage Facility: The store must have refrigerator & air conditioner in the premises. According to the labeling specifications certain drugs like vaccines, Sera, Insulin Injections etc. , are required to be stored in the refrigerator. Technical Staff:
Wholesale The sale of drug by wholesale shall be made either in the presence of registered pharmacist or in the presence of a competent person who shall be a graduate with 1 year experience in dealing in drugs or a person who has passed S. L. C with 4y ears experience in dealing in drugs, specially approved by the department of drug control for the purpose. Retail the sale of drug by retail must be made in the presence of registered pharmacist approved by the department, registered pharmacist is required throughout the working hours. Regards.

Requirement for obtaining Drug License
The following are minimum requirements for obtaining drug license or starting a pharmacy in India:
Area: The minimum area of 10 square meter is required to start a medical shop or pharmacy or wholesale outlet. In case, the pharmacy business combines retail and wholesale, a minimum of 15 square meter is required. Storage Facility: The store must have refrigerator & air conditioner in the premises. According to the labeling specifications certain drugs like vaccines, Sera, Insulin Injections etc. , are required to be stored in the refrigerator. Technical Staff:
Wholesale The sale of drug by wholesale shall be made either in the presence of registered pharmacist or in the presence of a competent person who shall be a graduate with 1 year experience in dealing in drugs or a person who has passed S. L. C with 4y ears experience in dealing in drugs, specially approved by the department of drug control for the purpose. Retail The sale of drug by retail must be made in the presence of registered pharmacist approved by the department, Registered pharmacist is required throughout the working hours. Regards.

No, entrance exam is not mandatory for admission to D.Pharma however many colleges admit students to a D.Pharma course via entrance exams. I have mentioned the admission process for D.Pharma below. D.Pharma Admission Process
Most institutes offering the D. Pharmacy course admit students based on performance in a relevant entrance test, often followed by a round of personal interview, wherein their general aptitude for the course is tested. Admission process generally varies across colleges. A few institutes also provide direct admission based on the candidates performance at the 10+2 level. Some of such entrance tests conducted in India are:
GPAT
UPSEE
JEE Pharmacy
AU AIMEE Pharmacy
CPMT
PMET.