This is rather a general question so I would try to cover as much as I can in one go.
Courses offered and Eligibility : Admission & Aid :: Undergraduate
Communication Channels: Try through Website but if it doesn’t seem to be working then you can call the departments in contact segment. I will get in touch with the admissions office and try to get their direct number. Give me a day or two.
Besides the above points, I recommend getting in touch with someone who just completed one year in Shiv Nadar University Undergraduate Program. In case you are not able to come around anyone then let me know and I will help you get in touch with one of them.
EDIT:
JEE is not mandatory but excellent marks in XII (80 percent is fine) will secure some kind of scholarship.