LPU - Lovely Professional University

You should start preparing for the CAT exams if you are looking to secure admission in any one of the Iims. Common Admission Test CAT is a national-level management entrance examination conducted by the Indian Institutes of Management (IIM). Apart from 20 Iims, CAT scores are used for admission to various management institutes across the country. Please refer to the article mentioned at the link provided below for important preparation tips from toppers of the CAT exams:
https://www.shiksha.com/mba/articles/this-cat-preparation-strategy-is-the-golden-ticket-to-success-blogId-14642.

If you are in the final year of mechanical engineering Diploma program then you are eligible for lateral entry exam in DTU.
All the best!

Yes, your distance education will be deemed valid for any further documentation and formal proceedings in your career. Moreover, I would suggest you to once go through UGC NET brochure as you need to match their criteria, eligibility and requirements too. Whereas, in the case of correspondence courses from LPU, your degree is valid everywhere.

Yes, you can apply for Canada for further studies.