Exam

No, you would not be allowed to sit in the university exam.

https://www.shiksha.com/college/department-of-management-sciences-Pune-university-pumba-ganeshkhind-30895
You will find all the true and authentic information about your college here.

NIFT lateral entry admission (NLEA) provides an opportunity to candidates who have completed their Diploma/Degree in relevant / related fields of Design & Technology for direct admission to the third semester of UG programmes of NIFT at NIFT campuses as listed in Annexure III. The candidates who have acquired Diploma/Degree will compete at an All India Entrance Exam to get lateral admission in the 3rd semester of UG Programmes of NIFT
The admission to these candidates will be strictly on merit which will be prepared based on the performance of candidates in written test, studio test/technology aptitude test, and a Personal Interview.

Yes, CUECT is among them.

Your academics are good. You'll get a good college but if you want best college then go for CAT/GMAT/GRE.

Yes, you can get.

Stanford Graduate School of Business
Harvard Business School
Instead
University of Pennsylvania: Wharton
CEIBS
London Business School
University of Chicago: Booth
MIT: Sloan
Columbia Business School
University of California at Berkeley: Haas
Yale School of Management
EM-LYON (Early Makers Lyon) Business School, Paris
IESE Business School
University of Oxford: Said
Northwestern University: Kellogg
Dartmouth College: Tuck
University of Cambridge: Judge
National University of Singapore Business School
HKUST Business School
HEC Paris
Duke University.

Yes, the DSE Pondicherry conduct TET exam every year.

First, get a detailed plan for studies. Fixed studying hours. Maintain regular notes. Restudy the completed topics. Confidence in you.