Mechanical Engineering

Yes, you have a chance to get admission in mechanical branch in best engineering college.

RV College Of Engineering, Ramaiah Institute Of Technology, BMS College Of Engineering, The National Institute of Engineering-Mysore, PES University-Bangalore, Dayanand Sagar College of engineering are the top colleges for mechanical engineering that you can get through KCET.

Your chances are almost nil as your marks are very low, still you can check out the below for details:
https://www.resonance.ac.in/reso/news/JEE-Main-Branch-Predictor.aspx

Last year, it was 384 for CSE and 346 for mechanical at Pilani campus. So, as the cut-off marks increase each year, this year, the cut-off may be 385-390 for CSE and for mechanical, it may be 350.
In case of Goa and Hyderabad, it is enough if you score 350 to get mechanical and CS. These are from my side, but no one can predict the exact cut off marks until they are released officially by the BITS admin.
The following link gives you the cut-off marks for the year 2016.
http://www.bitsadmission.com/cutoffscores.aspx
All the best.

Yes, PGDBM would be helpful to you, more so if you do it through regular ode of education from a reputed institution.

It's not one of the best. What are your other options?

Both are evergreen fields of engineering in every terms.
But Choose the field in which you love to work, you are very much interested in it and you have very much curiosity of it. Don't follow the craze. Go for your interested field. Trust me by this you will have more scope than any other fields and you will be successful.