CA

Both courses are equally good. CA is a professional course and pass percentage of successful candidates is low. It gives you opportunities to do a corporate job or independent consultancy. MBA is a generic course. Unless you do MBA from top 20 colleges of India, it may not give you stable & high salary job. If you do not have patience to work hard and clear CA it is suggested that you may go for MBA.

Yes definitely and that is a good choice too

BBA is a management course while CA and CWA are professional courses in field of commerce. So it is advisable to pursue MBA after completing BBA. Besides, most students prepare for CA & ICWA while they are still in Class 12, so that they don't lose out on the years.
Pursuing Bachelors and Masters Degrees in the same field will help you to have a strong foundation in a particular area of study.
However, if you are interested in doing CA or CWA then go for it. The choice of course depends on your interest and aptitude.

As per ICAI Norms, a CA Student undergoing CA Articleship is allowed to pursue . Form 112 for obtaining permission of ICAI to study additional course along with CA . to pursue the additional course through correspondence or Regular College. . permitted to attend college for any classes of any course (incl. graduation).

CA and BMS seems no relevance. Request you to do either ine of them. CA is tougher course and BMS is an easily obtainable degree. Both have der own opportunity, but CA has broader scope

Yes you can just do registration under icai for first exam I.e. cpt and take coaching.