B.Com

Dear Rohit,
As per AICTE norms, BE/BTech courses can't be done through distance education,
Although considering your graduation, you can proceed for an MBA degree which will give you a more detailed knowledge and skill sets on management.

You will have to apply for entrance exams like CAT, CET, ATMA, MAT, CMAT, etc. and the college will be allotted on the basis of your percentile.

Yes, you can do it. A long break is not a barrier to pursue B.Ed if you have a minimum of 50% in your graduation.