M.Tech Computer Science and Engineering

Both are different of fields. You should go in which you have pursued B.Tech. You should do M.Tech with the same branch that will enhance your knowledge in same field and really help you out for the good future.

I'll refer you to join B.Tech CSE rather than integrated 5 year course because if you change your mind in 4th year of your graduation seeing that time scenario then it will be better for you to join MBA or by qualifying GATE you can join any of the PSU because joining integrated course is only beneficial if you have clear goal to join in research or be a professor in any college.

Yes, you are eligible. For more details, check the link below:
https://www.shiksha.com/arts-fine-visual-performing/course/m-a-meerut-college-272301

Go for MANIT CSE or B.Tech CSE programme instead of any dual degree at other institutions.

It doesn't matter on the course. It matters on your ability, how talented you are, your communication skills, your technical skills.
Both are good.
From my suggestion, go for B.Tech+M.Tech.

https://cbsenet.nic.in/CMS/Public/View.aspx?page=80
Yes, but be sure that your percentage is at least of 55% in your Master's degree. Please check on above link you will get the details. It is official site also.

GATE qualified candidates can follow the following procedure to apply in IPU for M.Tech CSE:-
1.Apply by filling the application form first. The last date of filling the application form is May 1, 2018.
2. After having filled the application form, a merit list based on different scores will be issued by IPU. Keep yourself updated about the merit list by visiting http://www.ipu.ac.in/
3. Based on your gate score you will be called for counseling most probably in June/July.
Hope this helped :)