St. Xavier's College

No, there is no entrance exam for getting admission in B.Com in St Xavier's School, the minimum eligibility criteria is the college offers BA, B.Sc and B.Com as UG courses. The minimum eligibility for the courses is that the students should have passed with minimum 45% of marks in HSC or its equivalent from a recognized board.
The application form can be filled online for BA and B.Sc, while the form for B.Com has to be submitted through offline mode. The admissions are merit based and subject to availability of seats.

College does not offer BCA (Bachelor in Computer Application) course. A very similar and equivalent Bachelor's degree course is offered here. It is B.Sc in Computer Application. There is no cut-off declared officially. Cut-off varies every year. It depends on the performance of the candidates in the entrance exam that year.

Yes, St. Xavier's College provides BCA course.
https://www.shiksha.com/it-software/course/bachelor-of-computer-application-st-xavier-s-college-ranchi-329911

Yes, this college provides BSc in computer science. So, you can go there and ask for more details.

Mass communication course is not offered in St Xavier's College.

Minimum percentage requirement is 45% for taking admission in St. Xavier for B.Com course.

Yes, it is a full time course.

You can refer Guide for BBA/BBS/BBM 2019 (English, Paperback, Arihant Expert), BBA entrance complete book paperback 2018-By Chandresh Agrawal (author), Chandresh Agrawal & Nandini books (editor), BBA/BCA/BHM/Integrated MBA Exam Guide by RPH Editorial Board Paperback, etc.

Yes it is mandatory to pass in all the subjects to go for any college you want. You cannot proceed ahead, if you don't pass.