Which is more recommendable? Doing a BBA and a MBA or doing a BCOM and a MBA? I want to work as a investment banker?

Since you are bound to an MBA, it doesn't really matter whether you choose BBA or B Com as your graduation. But since you wish to work as an investment banker, a B Com will put you into the accountancy orbit, while a BBA will bring you closer to a business track.

It really does not matter. Ensure that you score at least 50% in your final year of graduation, since this is the basic eligibility to appear for the CAT exam. Also keep in mind, that most of the reputed B Schools accept only CAT scores

Preferable is B.Com- MBA. This will equip you well to work in banking sector. There are many universities that also offer integrated degree of B.Com-MBA, you can go for it too as it has its own benefits like fees, no trouble of searching for a college for higher degree and so on. Good luck.