D.El.Ed

You are not permitted by law to enroll in two normal courses at once. This is not a factor. In India, though, everything is conceivable. If you personally asked me, I would have to reply that you could accomplish it from a lesser-known university.
The biggest restriction is that you cannot present both your degree and Diploma when applying for government jobs or during other interviews.

The main difference is that one course is D.El.Ed is a Diploma level course while the other is a degree course.

 B El Ed's full form is Bachelor of Elementary Education. D El Ed Full Form is a Diploma in Elementary Education.

The Diploma in Elementary Education is a 2-year full-time course, mandatory for all teachers who wish to teach at primary or secondary schools (classes 6 to 10). The minimum eligibility required to receive admission in a course offering this Diploma is to pass standard 12 from a recognised board or school.

In government colleges, institutes or universities, the fees for the BTC may be between 8,000 to 40000. But in the Private Institutes or Semi-Government Institutes, the fees will be between 8000 to 85000 or even more. Each state has a different criteria.

Fee is Rs 25,000/- per year at St. Joseph College of Teacher Education For Women, Ernakulam.

Yes, D.El.Ed is valid for Madhya Pradesh Varg 2 exam. It is a Diploma that covers the educational and developmental aspects of teaching. If you are trying to qualify for the Madhya Pradesh Varg 2 exam by getting D.El.Ed and a teaching qualification, I would suggest you to approach a training center.