Mechanical Engineering

If you want to study in the best universities in USA, you need to pay a hefty amount as education is not cheap in USA. But there are some universities which provides education at a little cheaper fees which include:
University of Utah
University of Texas at Dallas
University at Buffalo
Texas A&M University
As a second option, you can consider about studying in Germany. It is the best place to study mechanical engineering without any tution fee. You will need to spend only around 15 lakhs. All the best.

Both engineering branches are good, but automobile engineering has good scope as compared to mechanical engineering.

You should opt for Germany as education cost is cheaper in Germany as compared to Canada. You have more job opportunities there particular for mechanical engineering. You need to learn the German language for that. Though Canada is good for Masters but it's more costly as compared to Germany. Canada is preferred for CSE.

Both the branches have great prospects in Karnataka, and in India too.

Mechanical engineering is a better option.

You can check out the link below for details on CEED :
https://www.shiksha.com/ceed-exampage
Opt for the branch that you love the most and are most passionate about. Analyze the future work conditions, scope and growth prospects before taking admission. You can also opt for psychometric test comprising of aptitude, personality and career interest to clear the confusion.

The cutoff for 2nd year admission is 60%, without any reappear in COEP or any college.

If you score well in IELTS and GRE , you have chances, but it's tough to get admission ,most of the applicants have good marks ,they need 75% mainly ,try to search more safer universities in Canada, like Newfoundland, York, Victoria, Laval, etc.

After class 12th, you need 6 bands overall in IELTS with not less than 5.5 in any module.
So, your 12th percentage and IELTS score seems perfect to me.
Get yourself enrolled in Bachelors degree, you will get the visa.
All the best!