Distance/Correspondence

No, exams are not open yet you may apply to it by entrance forms after July.

https://www.shiksha.com/medicine-health-sciences/dietics-nutrition/course/diploma-in-sanitary-inspector-imperial-institute-of-management-andheri-west-mumbai-288689
Here is the complete details of the course of nutrition and dietitian for this college

If you are university is approved by UGC then definitely you are eligible to apply for both the Government and Private sector job. But, most of the private sector companies which do not prefer the candidate who has completed their graduation through distance mode. After completing B.Sc (PCM) you are eligible to apply for National Level and State Level Government exams.
1) Union Public Service Commission (www.upsc.gov.in)
2) Civil Service Exam (www.upsc.gov.in)
3) Staff Selection Commission (ssc. nic. in/)
3) Other State Level Government exams.

JMI B.Ed programme Distance Mode - Admission is through Entrance Test. Applicants must be In-Service Teachers with (I) A Bachelor's Degree (10+2+3) from a recognised university, (ii) Two years full time Teaching Experience on Temporary/Permanent basis in a Primary; Secondary/Sr. Admission is through entrance test.

What is the eligibility to get admission in Criminology courses?
To get admission in this field you must have cleared the 12th examination with science subjects.For admission in B.A degree program in criminology or cybercrime, a student had the art group in 12th can apply.

If your distance degree is of recognised University and approved by Directorate of Distance Education. Than you can take admission in desired Master course anywhere in India.

Yes of course you can apply for it as for distance courses you can apply anytime.

Different students have different reasons for studying MSc in Distance Education mode. MSc can be done in various fields like Technology, Computer Sciences, Botany, Zoology, Mathematics and so on. There are number of Universities in India that offer MSc Distance Education.

Law Courses after class 12th
Bachelor of Laws (LL.B.) 3 years
Integrated undergraduate degrees B.A. LL.B., B.Sc. LL.B., BBA LLB, B.Com LL.B 5 years.Master of Laws (LL.M.) one/two years.Master of Business Law. Doctor of Philosophy (Ph.D.)Integrated MBL-LLM/ MBA-LLM 3 years.