GMAT

Yes, any good university will ask for a GMAT score though there could be exceptions. Check Thompson Rivers University or Vancouver Island University, they don't ask for GMAT.

A 750 GMAT score, solid work experience with demonstration of excellent leadership skills, strong career goals essay and an overall strong profile should land up in top ranked business schools like UCLA, INSEAD, LBS, NYU, KELLOGG, etc.

For current PGPEX batch, GMAT cut off is 717.

No, only work experience won't do. For the current batch, GMAT cut-off is 717 and the minimum work experience criterion is 5 years.

Hello Abhimanyu,
You may refer the link below for the list of top management institutes in India :
https://www.shiksha.com/mba/ranking/top-mba-colleges-in-india/2-2-0-0-0

It is impossible to get admission into a "good" college anywhere in India for studying MBA without appearing for any entrance exam. So you need to give one or the other exam, clear all its necessary cutoffs and perform well in the interview rounds(if shortlisted).

This year CAT will be conducted by IIM Lucknow, check the IIM L website for further notifications.
For MAT - https://www.aima.in/testing-services/mat/mat.html
For XAT - http://xatonline.net.in/
GMAT - http://www.mba.com/india
Keep checking these websites for registrations and online application forms.

Hi, lets answer your question point wise
1. No all exams are not necessary, take either of GRE or GMAT and one from TOEFL or IELTS.
2. University of British Columbia - Sauder School of Business, McGill University - Desautels Faculty of Management, York University - Schulich School of Business, Western University - Ivy Business School, University of Toronto - Rotman to name a few
3. Yes, work experience is mandatory except a couple of bottom ranked universities.

As you finish your second year of BBA, you have to write IELTS exam in your third year then meet the consultancy then proceed.