Lateral entry

No, lateral entry in MCA programme is not available at the asked college. The MCA eligibility criteria is given below:
Eligibility : Passed a 3-year Bachelors Degree programme in any discipline with mathematics at 10+2 level or
passed 3-year Bachelors Degree programme in any discipline with Mathemati

As per Information brochure-2019 of TNAU, the B.Tech (Agriculture engineering) lateral admission are not available.

New Delhi Institute of Management offers only Masters and Doctorol management programmes (PGDMs and PHd). Hence BBA program is not available here.

Lateral 2nd year admission are available in B.Tech Marine Engineering at Mumbai, Kolkata and Chennai campuses. The eligibility criteria is as under.
Eligibility for Lateral Entry : Candidates with at least 55% marks overall in: 3-years Diploma in Marine/ Mechanical/ Electrical/ Electrical & Electroni

Yes, you can do it. Below is the link to get all the details about the admission process, kindly visit the link:
https://www.shiksha.com/university/dtu-Delhi-technological-university-dce-23920/admission

Yes you are eligible. As per the eligibility criteria of M.Sc. Computer Science (Software) (2-Year) Part-II
the candidates having passed M.Sc. Part-I in any area of Computer or 1-year Diploma course after
Graduation in any area of Computer from this University or any other University/Institute/DOEACC

IITs and NITs does not offers admission in B.Tech courses through lateral entry for Diploma engineers. You should seek admission in Maharashtra state Engineering Colleges through CAP rounds conducted DTE Maharashtra. For more details visit http://cetcell.mahacet.org/

I guess having maths is not at all compulsory in determining whether you will be able to study PGDCA or not. And yes, you can go for lateral entry.

Yes, to get a more detailed analysis of the names and details o the colleges that provide the courses you can try out shiksha's official college predictor.