BCA

Yes, it is. But, you need to fulfill the eligibility criteria to have mathematics as one of the subject in class 12th and should maintain minimum 50% in class 12th.

The eligibility criteria for M.Sc in CS is 2nd class honors or above in CS at graduation level. You can go for MCA.

Yes, you can opt for animation course along with your ongoing BCA degree program, provided you can manage both the courses well, which indeed is going to be tough as both the courses demand great amount of concentration, practice and knowledge build up.
There are many courses available in animation stream, yet I would suggest you to go for a Diploma course instead of a degree program to begin with. However, you can later opt for upgrading it or simply go for advance/ higher courses in animation field.

Hi,
You can pursue BCA or web designing. Both the courses have ample opportunities and it depends on your interest and dedication and if you like to pursue web designing, so there are different institutes, coaching class and academy.

In case your programming skills are not good and you are sure about not making a technical career then MBA is an excellent choice to switch career. You are advised to prepare for prestigious MBA entrance exams such as CAT, XAT, MAT, SNAP, IIFT, IRMA etc.

You can take up MCA or else MBA. Both has good opportunities and it's up to your interest overall.

Since you are from BCA background MCA is preferable. MBA is quite different from BCA terms. It's up to your interest then.