BCA

You are advised to do BCA from a college which has good computer facilities, good teaching faculty and placement records if the location is not a personal constraint for you.

Yes, you can do BCA after 12th with commerce background. You are eligible. Some university demand for an eligibility certificate for commerce background. Normally, commerce student's maths & technical side is weak and BCA require both the things. You have to face 2 maths subjects during BCA and learn various programming languages. So, if you're really interested in computer programming and can face maths subjects than go for BCA otherwise don't change your stream and go for managerial courses like CA, CS, BBA, B.Com, etc.

If you are interested in computer programming and having good programming skills then go for BCA or else go for BHM, it is good.

You can take either commerce with maths or science stream- PCM (physics, chemistry, maths). Also, you can get computer science or information practices in both of the streams which can help you in BCA also.

No, DU doesn't offer technical courses like BCA.

B.Sc is general course but BCA is professional course based on IT. BCA syllabus made to grab a good career in the IT field. So, BCA is the best option for today's market.