University of Mumbai [MU]

I would necessarily say St Xavier's College Mumbai is much better than say DU. As here you get an all-round exposure apart from studies. And I personally believe that the kind of personality development you would get here at Xavier's is beyond any colleges of DU unless you go to Stephen's, LSR, Hindu etc.

You have to make an affidavit of gapping year as per university norm document.

Kindly predict your college in this college predictor. JEE Main rank predictor is an online tool which predicts the candidates rank range and probable colleges based on the difficulty level of the examination, average marks scored in JEE Main and seats available in IITs, NITs, GFTIs, and other SFTIs. The rank predicted might not be accurate but it certainly does give an idea to the aspirant. Know your college admission chances based on your JEE Main Rank, Home State, Caste, Gender, etc. here:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

No, post graduation admission will start from mid of June. You can apply for admission then. Good luck.

Yes, the admissions are open for 2019.

Yes, since you have done masters, now you are very much eligible for dietician and nutrition course. It is an upcoming field and you can grab number of job opportunities after this course.
All the best.

Yes, this university is good. You will get to learn new things here. They have helpful and friendly teacher. You can take admission there. You will get good opportunities ahead. Good luck.

Here you can find out all the courses provided by this university.
Kindly follow the link:
https://www.shiksha.com/university/university-of-mumbai-856

You can take distance education from here. This university is good for distance learning.
Good luck.