Diploma

No, you cannot do master of business administration (MBA) directly after diploma. Diploma is equivalent to +2 and MBA is post-graduation course. For admission in MBA course, you'll need to be a Graduate at least, as this is a Masters or Post-Graduation Program.
With a Diploma in Engineering you 1st need to complete your graduation. If your interest lies in engineering you may go ahead with engineering course many colleges admits Diploma holders directly into the 2nd Year of the Engineering course through lateral entry examination conducted by various engineering colleges.
If you don't want to pursue Engineering any further you may take up BBA course which gives you a hint of all the factors related to Business Administration post which you can decide which stream you want to do your MBA in (MBA is offered with specialization in fields like - Marketing, Finance, Supply Chain, Operations, IT, Environment, Health and Safety, HR etc.).At the same time you can prepare for CAT, MAT and XAT to get college of your choice.
All the best.

First of all, congratulations for your diploma. Now, coming to your question, one can only join any college for Bachelor's in the first year after his/her 12th through entrance examination or in merit basis. And in 2nd year, through lateral entry. No college offer direct admission in 3rd year of engineering. I have never heard so. You should keep yourself away from these types of myths. You should focus on your subjects and appear in graduate aptitude test in engineering (GATE) which is a national level engineering entrance examination. On the basis of graduate aptitude test in engineering marks, you can take admission in various reputed colleges of India for Masters Course. You can prepare for CAT to take admission in MBA colleges. I will suggest you not to change college. Dropping a year for better college may be a good choice. You may take a year drop and appear in lateral entry examination conducted by various colleges. If you want to complete your B.Tech from a centrally funded college, then I will suggest you to join Hemvati Nandan Bahuguna Garhwal University. Fee per semester is very less there (11000 per sem.) Rest is your choice.