DTU - Delhi Technological University

DTU is a better option than MNNT, Allahabad.

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.

DTU is better than NSIT. U should prefer DTU over NSIT . It gives much better placements and academics compared to NSIT.

All the core branches are available in the DTU, Delhi but the GATE cut-off is very high in all the branches of this college.

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.

First, you need to clear JEE Mains exam with a high rank. Then, after the counselling, you will be allotted a college.

Hello, you can check syllabus by clicking on this link. https://www.shiksha.com/b-tech/exams/haryana-leet/syllabus.

Hello, you can check syllabus by clicking on this link. https://www.shiksha.com/b-tech/exams/haryana-leet/syllabus.

Yes, you are fully eligible for the scholarship but you have to clear some test and some formalities. For more information visit the link below: https://www.shiksha.com/university/Delhi-technological-university/exams/dtu-leet.

Yes, you can. Refer the link for details: https://www.shiksha.com/b-tech/course/b-tech-in-electronics-and-communication-engineering-delhi-technological-university-rohini-52813.
All the best.