hello,

for doing ME in Mechanical engineering , you have to do BE in Mechanical engineering. for admission into ME, you have to appear GATE exam and get decent score to get admission into colleges.  after ME (PG degree), you will have high chances to join as a professor.

your chances will increase if you will do ME from top IIT or NIT campus. for job option, you will have to look for job post from institute/university campus webpage.

Hope it helps!