online B.Tech

Dear friend, as per my experience and knowledge, B.Tech in 4 Year programme and MBA is of 2 Year programme, whether you do online or offline. It depends on you, but as per my views there is no online facility for these courses, you have to go in universities and get admission into it.

The exam pattern of NATA 2018 also states the type of questions that will be asked in the entrance exam, which will be conducted in online (Part A) and offline (Part B) modes.

The exact dates for entrance exam forms availability is still not out. For more details, check out the link below:
https://www.shiksha.com/science/course/m-sc-in-food-science-and-technology-shivaji-university-maharashtra-other-285998

Yes, you can take admission but after admission, you have to show your certificates to the institute (when you receive them) for further verification on the day of joining the institute.

In India few Business Schools offering MBA in Agri Business. Like IIM A, SIIB and Others. IIM A admission through CAT & SIIB Admission though SNAP Test. You can take CAT Exam and score very high percentile then have a chance to get good Management Institutes.

Please specify the name of the college. Mostly, for all the colleges, admissions are closed for Masters programme. The session has already started.

Which application form? You have not specified that.

Evening/distance/online engineering courses are not valid anymore as per the latest supreme court verdict, hence I would recommend you to join a regular B.Tech course for better career prospects.
http://www.tribuneindia.com/news/nation/no-technical-education-through-correspondence-says-supreme-court/491819.html