Guru Gobind Singh Indraprastha University

All three branches are relatively similar. All deals with the mechanical part of engineering.
Though in automobile engineering, you mainly deal with engine and motors of vehicles.
Whereas in mechanical engineering, you deal with every aspect of mechanics that is there.
Mechatronics is a combination of mech and electronics where you deal with combined electronic and mechanical aspects of things. This is a relatively newer branch and should be pursued from good institutes only.

The eligibility score for admission in B.Ed. programme is at least 50% marks (i.e. aggregate of total marks in all subjects offered by the candidate) either in the Bachelors degree and/or in the Masters Degree in Science/Social Science/Humanities/Commerce, or Bachelors in Engineering or Technology with specialization in Science and Mathematics with 55% marks, or any other qualification equivalent thereto.
So I think you are eligible.

Yes, surely, you can good any good IPU College. Your rank is pretty good. Try for top IPU colleges.
All the best.