DTU - Delhi Technological University Answered Questions

The last date to apply is over and currently the third round of counseling is in progress. So you will be able to apply next year now. You can check about ongoing process here.
http://admission.dtu.ac.in/bt_le_eve/registration.php
Also, you can approach the college you seek admission in to know whether it has management quota or any seats are vacant there.

For private jobs, yes it matters. They will want a candidate who has academic exposure and has some early experiencing field that is gained through internships. You will be able to study at home, but for internships you will have to work under an institute. So, a regular student will be prioritized in a private job.