D.El.Ed

Yes, you can. D.El.Ed. can be done through correspondence.

No, need. By the way both D.El.Ed, & BTC (not TBC) are the same courses.

At a time you cannot pursue two courses under same or different universities, according to the rules of UGC. So you have to wait for completion of your B.Ed.

Both courses are designed for Elementary Teacher Training i.e. upper primary (Class VI to VIII). You can join D.Ed or D.El.Ed course after class 12th (Senior Secondary).
If you qualified D.Ed or D.El.Ed after 10+2, you can apply in TET Exam (Paper I) I.e. for Primary Stage teachers.

JBT is similar to D.El.Ed. (Diploma in Elementary Education) course. JBT and D.El.Ed courses have a similar syllabus, course structure, and career prospects.

Yes, you can do D.El.Ed. Later, you can do your D.Ed also. But, you are advised to clear your +2. Otherwise, there will a big gap in your learning .If your learning is incomplete, how will you help your students in future?

No, you need not do D.El.Ed again. It is required for those teachers who are teaching in government schools without any training.