Regular and distance mode courses together

Since, you are persuing the courses with the different universities and the time of examination does not coincide to each other, you can persue the same.
It is essential to verify the UGC status of both the universities it means these universities are recognised by the University - grant commission. The universities with which you are persuing the courses are recognised and are having UGC affiliations.

The Distance Education Council (DEC) has decided that though students cannot pursue two-degree programmes simultaneously, they can pursue two programmes simultaneously through distance or combination of regular mode and distance mode.
As you are doing B.Ed in regular mode, you can't do M.Sc in regular mode. But you can do M.Sc through distance education mode. In such case both the degrees are valid provided both the institutes you are studying ate having UGC approval.
In your case, you will complete your B.Ed in 2020 and M.Sc will be completed in the year 2011. There will not be any problem in this case also.

This had been brought to the notice of UGC from time to time in the past and matter was deliberated in detail.

Presently the legal position in this matter is as follows.

A student can not join two regular courses simultaneously. So practically speaking they should not overlap also.

But at the same time, a student can have one regular course and one correspondence course.

There are some learned educationists in our country who are advocating and pleading to UGC to allow even two regular courses to the capable students to be undertaken simultaneously but UGC has not agreed to it.

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.

As per the existing guidelines in the matter, one can not have two regular courses to be pursued simultaneously. There are other issues also like clash of the exam dates or other inconveniences.

At the same time as per the present regulations, a person can opt for one regular course and one correspondence course. So you can make the plan as per these guidelines only.