Computer Science and Engineering

No it is better to do BCA only, then choose upto your interest.

https://www.shiksha.com/college/zakir-husain-college-of-engineering-and-technology-Aligarh-50219/admission
Here is the complete admission procedure for getting admission in this institute.

The basic criteria for getting admission is to get a minimum of 60% in your 12th PCM. After that, you can now Apply From The Convenience Of Your Hometown If You Have Appeared in National/State Engg Entrance Exam. You can submit the Entrance Exam score and Statement of Purpose ( 1-minute SoP video )

yes. mathematics is a must in class 12 level if you want to apply for bsc in computer science. although the requirements vary you can chave a check at the respective college.

yes absolutely. you can continue your third yeear since bsc course duration is only of 3 years and you cannot get the degree by studying for 2 years.

You have to give the GRE examination if you want to do MS from other countries and then score at least 330 out of 340 to get a scholarship or funding.