CAT

A minimum of 75-80% marks is required to get shortlisted for GD-PI. Rest, their trends change every year. All the best.

It is relatively easy for engineering students because of good mathematics. As CAT tests your verbal and analytical reasoning ability, so, your engineering background will be helpful for you. You may download the syllabus and previous year question papers from any IIM website to get some ideas about the CAT.

You have to score above 60 percentile in CAT.

Cut-off does not matter for PGDM course as it is open for all India level seats.

You are advised to seek a job to gain some experience and try for CAT, XAT, MAT, SNAP, NMAT, etc. with two to three years of experience.

You need to contact their official website.

Yes, students prefer MBA after B.Tech. Most companies prefer management plus technology aspirants.

Although, it is too late as almost every college worthy for your percentile had closed their admission process. You can give upcoming MAT exam and try for some better colleges. But still if you want some names then here are they:
1. UPES, Dehradun
2. VIT University
3. Great Lakes Institute of Management
4. Myra
5. Alliance school of business
6. Galgotias
7. JK Business School

You may not get a good college but there are colleges which will give you admission through Institution donation quota and if you are planning to get admission, you can still give ATMA-May and MAT-May exams.
All the best.

Mostly the preparation is similar to CAT and since the exams aren't that far, there is nothing additional to be done for XAT. You have to solve a lot of sample papers to get a feel of the format and the level of questions expected.