CBSE 12th

The eligibility criteria of BA (Hons.) Economics of LSR (University of Delhi) is given below.
Eligibility criteria :
1. An aggregate of 45% marks in the qualifying examination.
2. The merit shall be determined on the basis of one language and three best academic/elective subjects.
3. The applicants must have studied and passed Mathematics at the qualifying exam for admission to BA (Hons) in Economics.
So, Mathematics is mandatory here for BA (Hons.) Economics, Hence admission is not possible.

The eligibility criteria of MBA course is a Bachelor degree in any stream with minimum 50% of marks, while the admissions in MBA courses are based on percentile obtained in Management entrance exam scores like CAT/MAT/CMAT/XAT etc. So there is no need of Math in class 12th, you can complete your class 12th and graduation in any stream.

The probability of not getting admission is high. But, would suggest you talk to the kiit officials through the number given on their sites as there might be chances that they have changed their norms.

You can pursue M.Sc after completing B.Sc.

No, you do not have to give any entrance examination for taking admission in IGNOU for B.Com course. Good luck.

Yes, you can pursue your undergraduate course in New Zealand.