BCA

The B.Sc (CS) course mainly focuses on the mathematical and theoretical foundations of computing, rather than teaching specific technologies that may quickly become outdated. This course prepares you for higher education.
BCA is more professionally oriented; it prepares you for post-graduate or research work and also creates professional manpower for problem solving through application of computer science at the interface of business and technology.
If you want to join Indian Army after BCA, you should give CDS entrance exam as it is for officers post in army, you can join Army after clearing CDS.

After 12th, you are eligible to apply for BCA course without mathematics. The eligibility for the BCA course is 12th passed with minimum of 50% marks. But you will face some problems without having maths in BCA as after its completion, you can't take admission into MCA as you don't have maths in BCA as well as in 12th.
However, many colleges/universities offers MCA degree courses without mathematics. So don't worry about it.

In case you want to become a software developer in Indian IT companies then you must plan your education minimum up to MCA. In the meantime you can learn one of Object Oriented Programming language such as C#, C+ or Java along with your graduation degree. Also you are advised to learn at least one RDBMS and database programming fundamentals.

Yes, you can. You need to have a graduation degree in order to pursue MBA.