Colleges in Delhi

DTU blindly. It comes just after IIT Delhi.

Yes, that is a mandatory thing!

They are about to start soon. Stay tuned and do the visit site regularly.

http://www.dtu.ac.in/Web/Admission/b.tech(LE).php
Check out here. This information is during 2016-17. For upcoming session, wait till they upload on site.

Yes, the eligibility is 45%.
https://www.shiksha.com/humanities-social-sciences/course/b-a-hons-in-applied-psychology-dr-bhim-rao-ambedkar-college-yamuna-vihar-delhi-53883

You must have a Diploma degree after completing 10th before applying for admission in DTU.

IITs, DTU and NSIT.

You can't just describe a college to be best upon the placements (reason I will explain below). Also the course structure of event institute are also something they are experimenting with the students at this moment.
So I will try to be very specific upon the topic about best institute. There are a number of institutions available with different courses in the market. The institute are like:
NAEMD
NIEME
MDI
Amity University, etc

Check the difficulty level. Analyse the question paper considering past years' question papers. Check sites of various coaching institutes because its not easy to predict cut off for JEE Advanced like Mains. JEE Advanced cut off fluctuates more than Mains.