Distance/Correspondence

Yes you can join the college in second year. It's doesn't not effect in which manner you completed your first year. Distance learning is a best way of learning but it can't have a comparison in offline college. So connect to you college at once. So they can guide you properly. And as per I know you can easily join the college in second year.

Yes, you can do PG master of hospital administration from a regular college.

Distance LL.B. Is not valid for practise.

Yes, there are many diplomas available for nutritionist after your 12th.

Yes, one can do a Ph.D. after a distance MBA. The institute must be recognised by UGC. Universities cannot differentiate between the degrees. The degree earned must be in tandem with the degree mentioned in the eligibility criteria
Colleges Offering Distance Learning MBA
Symbiosis Centre for Distance Learning. Indira Gandhi National Open University, IGNOU. Sikkim Manipal University- Distance Education, Sikkim. Amity University.

A valid score in any of MBA entrance exam like State Level CET/ MAT/ CMAT/ CAT/ ATMA/ XAT or equivalent management entrance test. Some colleges may conduct their own entrance test if you don't have any other test score.

MBA Distance Education Admission: MBA Distance Education is a 2-year master-level course that is offered for admission to students who have an interest in making a career around the management prospect, those who are unable to attend a full-time MBA programme due to financial or work constraints should consider a distance MBA programme.

Jyoti Rao Phule is a government university which does not have CPLT, If you want to do that you can do it from private University.

If you want to do MBA with job then online mode is best.

So, having completed your B.A. Degree course even in distance mode, you are eligible to pursue MBA degree course if your college is approved by UGC for distance education courses. Also, for pursuing MBA degree course from good business and management schools, you need to qualify MBA entrance examinations such as CAT MAT XAT GMAT etc.