Manipal Institute of Technology

Mechanical engineering is really good at Manipal Institute of Technology. The faculty is also very skilled and there are amazing labs for practical experience in the branch. There are a lot of clubs relating to mechanical engineering as well.

There is a different cut-off for each branch. You'll find them online on Manipal website.

CSE cut-offs are usually very high. With 104/200 you'll probably be eligible for Aeronautical, Automobile, Biotech, Biomedical, Print and Media Technology and Mechatronics.

Manipal University has no institute in Bangalore. It stands firm in Manipal,Jaipur and Sikkim in India .

Being an Aeronautical student herem in Manipal University, I can tell you, it is 100% sure to get the same course with such a good score. cut off is somewhere around 90 for aeronautical in Manipal University.
Getting a scholorship is a bit difficult with this score, but seat can be confirmed in the first round itself.

Yes, you are 100% bound to get aeronautical engineering in MIT.

60% marks is required in maximum cases.
Sometimes, it may be 55% marks.

SAT scores are not acceptable to get admissions in Manipal. Since your son is a US National, he does not necessarily have to give the entrance test. There is a separate direct admissions criteria for NRIs and foreign nationals since their academic curriculum is very different from general courses in Indian schools. The procedure for the same will be available in the admissions page in manipal.edu website.

To get a guaranteed seat in MIT, you'll have to score atleast 130/200.

You don't need to go to any specific book for the exam. Just brush up your Diploma concepts. The exam consists of basic mathematics, physics, chemistry and English questions. You'll find a list of topics that they ask from on the admissions page in the manipal.edu website.