Ramjas College, University of Delhi

https://www.shiksha.com/compare-ramjas-college-vs-hansraj-college-id-247485-52331
You will find all the true and authentic information about your college here. You can get the diploma course by getting good marks in your degree

Yes, Ramjas College comes under the Delhi University and full Delhi university comes under the CUCET examination. Admission in PG is done on the basis of CUCET Marks. You need to apply for CUCET when the application is released and after that you need to give the exam. And on the basis of your marks, you will be allotted the college. The more you score, the more chances you have to get in Ramjas College.

Ramjas offers a wide range of courses B.Sc. In core subjects, life sciences, B.A. M.A. Etc. Check this link
https://www.shiksha.com/college/ramjas-college-north-campus-Delhi-3075/courses here is the list of the courses offered by this college.

Yes, your 12th grade does matter a lot. Every year, the institution is among the top ten DU schools, with a high cutoff. Good luck and hard work.
You might attend Chandigarh University.

Both are excellent colleges of DU. I suggest to go for Ramjas College.

Yes you can pursue B.Com without Maths in any of the DU colleges if you meet the eligibility criteria.

You are true and it's expected that this time cut off will go time. Try in second and third cutoff. Infact I also want to add on that don't run for college, run for the course, the subject you love. DU has many good colleges and infact faculty in every college is very good.