Polytechnic

I don't think it would be really worth. You can pursue B.Tech instead of B.Sc. You'll get more value than B.Sc. holders and also, you'll get direct admission in the second year.

Once he missed he can't but you can wait sometimes authority calls again' for second third counseling if some seats are vacant.

No, you can't once you missed the submission date but you can apply in private college and ask them for direct admission.

Yes, now, you are late last date was 19th April 2018.

Syllabus for Diploma in Food Processing from DEI is-
Cookery larder importance
Catering establishments larder - organisation & layout.
Larder control
Methods of cooking with special application to meat, fish, vegetables, cheese, pulses and egg salads
Classification, balancing of recipes, standardisation of recipes,
Standard yield
Maintaining recipe files,
Fish roux balance, roux blond and roux bruno
Butchery, eggs, poultry and game vegetables
Assembling of cold buffets, sandwiches.
Theory of bread making
Different types of forcemeat and their uses
Pastry cleaning and care of larder equipment
Kitchen stewarding and upkeep of equipment.

Yes, your class 12th marks will affect your placement, but if you want to pursue Polytechnic with lateral entry, then this class 12th marks will matter. And, if you want normal Diploma, then it doesn't matter. And also, sometimes it depends on recruitment board or recruiter.

I think you should study class 11th, class12th and prepare for IIT-JEE.

JMI will be a good choice in my opinion, and as you have secured good rank there you should first go there. Keep IPU as a backup.

It depends on your choice and interests. Always think one more time before taking any decision. Best of luck for the future.