Indian Institute of Technology, Delhi

You are advised to compete BCA-MCA and then appear for GATE to seek admission in M.Tech Computer Science.

Go for FIITJEE or Akash. You can also opt for Bansal or Resonance in Kota.

No, it is not possible. IITs in no case provides lateral admission to anyone, not even accepts a college transfer from any institute even if it is an IIT. The only means you can get admitted into B.Tech programme of IIT is by appearing in JEE Mains followed by JEE Advanced.

IIT and NIT are the best govt college. IIT, Kharagpur, IIT Delhi, IIT Bangalore, IIT Mumbai, IIT Kanpur, IIT Rorkee, etc are some of the best IITs.

Please visit the placement report published on the website. All the details have been included in the same regarding the placements:
http://dms.iitd.ac.in/MBA 2017/Final Placement Report Batch 2015-17.pdf

You are advised to appear for JAM (Joint Admission Test for M.Sc) for seeking admission in M.Sc in IITs.

If you are only concerned about placement then go for IIT mandi CS, but if you are interested in other things and your overall development because at last money is not what you want, go for Physics, IIT delhi or Mech, IIT roorkee.

First of all congratulations! I will recommend you to go with CSE from IIT Mandi, but in that case only if you have a keen interest in computer science and engineering. Placement wise it's very good also you will get very good exposure. IIT Mandi has very good semester exchange program too, you have a very good option there to go abroad and explore further. Else if you wish to go with core opt for the other options which are left.