BBA

I am sure you can if you meet the admission requirements. They mostly have BA programs in business administration. Please visit university/college websites for details and admission requirements.

You are advised to appear for CAT in final year of BBA to join Government University for MBA. Government Universities such as Delhi University, BHU etc use CAT score for admission in MBA. Some Government Universities such as GGSIPU conduct their own entrance exams for admission in MBA.

Both are different streams, so comparing them makes no sense. Figure out what you enjoy studying most, figure out your skills - Do you like decision making? Do you have good analytical skills or do you like research oriented work? Take a psychometric test and check your aptitude. If you want an MBA later again, there is no point doing B.Sc. Choose the field you really like.

If you want to do CA, you should go with B.Com is much better. But if you want to go along with you BBA, you should have at least 60% marks in your degree to take admission in IPCC.

Christ University - Bangalore, Xavier's Kolkata, Symbiosis - Pune, DU are some of the best institutes to target for BBA. Check the below link for more-
https://www.shiksha.com/top-10-bba-colleges-in-india-article-7797-1

There are various colleges you can choose from and it again depends on your locality and other factors but yes BBA is a good course to do before MBA.

Yes, it is a perfect combination if you're looking for management roles, BBA is subset to MBA and has good designed curriculum suitable for management studies and professional.

You probably need graduation degree and need to appear for exams like GATE, probably you need more 6-7 years from now so that you can complete your graduation and gain decent work experience.