B.Ed

Hi,
As per my knowledge, it is not possible because when you are going to take admission at that time you have to submit your migration certificate.
If both the exam are going to be happen at the same date and time, then how will you manage? If you have interest in both, then please do one thing at a time among MBA and B.Ed.
Best of luck.

Yes you can, even if you are working.

Both the options are good. One of them is for marketing line and other is for teaching.

B.Ed and MCA are two different courses with different subjects.

It depends on what your priorities are. If you want to start your career as a teacher then go for B.Ed first. Then you will be eligible for TGT posts. But if you want to continue into research field then you should opt for an M.Sc and then try for a Ph.D. All the best for your future endeavors!

Yes of course. You need to have a Bachelor's degree in the related Science subject along with a B.Ed degree and you also need to qualify the CTET.
All the best.

It totally depends on you. If you think that you will go in the teaching line, then you must do B.Ed after B.Sc, but if you want to do research opt for M.Sc.