NIELIT Lucknow - National Institute of Electronics and Information Technology

Go through the link below for all the details regarding NIELIT Gorakhpur:
https://www.shiksha.com/college/national-institute-of-electronics-and-information-technology-gorakhpur-22175.

No, there is no entrance for the course. The eligibility to apply is you must have passed 10+2 or any Diploma (Govt. Recognized) of a minimum of 1 year duration after 10th class/ ITI Certificate (one year) after class 10.
or successful completion of the second year of a Government recognized polytechnic engineering Diploma course after class 10, followed by an accredited 'O' Level course concurrently during the third year of the said polytechnic engineering diploma course. The 'O' level certificate will be awarded only after successful completion of the polytechnic engineering Diploma.

Yes, if you are planning to get a job in the government sector.

First of all, congratulations on your success. Coming to the question for general category, it ranges from 30,000 to 40,000 (including hostel, library & connectivity) per year. If you are not financially strong, you can take an education loan.

'O' level course of DOEACC scheme is equivalent to a foundation Level course in computer applications. Students can acquire this qualification by undergoing 'O' level course and passing the examination conducted by the NIELIT. After completion of 'O' Level course, students can further enrol for DOEACC 'A' level course. You can only get computer operator job after 'O' level course.
B.Tech CSE is an engineering degree. It will help you to join a developer or tester job in IT companies. B.Tech CSE is far superior and higher degree in comparison to 'O' level certification.