M.Sc Economics

Yes, you are eligible you just need a graduation for Masters and B.Sc is sufficient for Masters in economics too.

You have not written about the college for better response. However the eligibility criteria of DU's is given below for an idea. B.Ed. Eligibility criteria of DU : Candidates with at least 50% marks in aggregate either in Bachelors Degree and / or in the Masters Degree in Science / Social Science /Humanities/ Commerce or any other qualification equivalent thereto are eligible for admission to the programme. Here M.Sc. Economics is falling under Social Science as per Table-1 of B.Ed. Prospectus 2020. Admission criteria : Admission test
So from above you are eligible for B.Ed. If meeting the aggregate percentage of eligibility criteria.

I think you should go with B.Sc. Statistics, because B.Sc. Data Science students have big competition with B.Tech CSE students and most of the companies prefers to select the B.Tech CSE students in place of B.Sc. Students.

Yes, there are some chances of getting a call.

Yes, you can. First, you complete B.Sc, you can choose any subject for masters.