As all the Universities in India have to follow the rules of U.G.C, they are linked to each other in a way. According to the U.G.C norms, one cannot obtain two degrees in the same year, even if they are from different universities.
You have to wait for your B.ED course to be over and only then you can apply and pursue the Master's degree course.
Actually, for NET/CSIR you won't need the B.ED, but your Master's Degree. They even allow provisional candidates who have written their PG finals and the result is yet to be declared. For that you need to show at least 55% of marks in the first semester.
Without writing your P.G exams, you will not be eligible to apply for the NET/CSIR.
So, I would suggest, first you have to concentrate on the P.G course and then apply for the NET/CSIR exam.