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You can do MBA in both finance or HR but for a better package, finance is good.

Definitely,
There is no restriction as such. Once, you have completed your under graduation, you are eligible to pursue your Master degree in any college or university with the required level of entry. MBA can be done through online, regular or distance mode.

CA does not require a Bachelor's degree.
It's a course which is self sufficient and you can complete it after clearing all the exams and other trainings as made by the Institute of Chartered Accountants of India.
A Bachelors degree is just an add on because no one likes to be called as an undergraduate.
Also, after you complete CA, you might get rejected when applying for government jobs, if you are not graduate, too.
So, think and act.
All the best.

Are you doing a job? If you landed a job then you should work in a company for 3 years then you can do MBA as work experience is important for MBA.

If you want to do MBA after your Bachelors, go for BBA. It'll make it easier.

Yes, you can get it but you have to wait for the list. And if you are a resident of Delhi, then your chances are better. Last year, some seats are remained vacant, this may happen this year also and you may get it easily.