NIT

I think the counselling process starts from the first week of July.

You can't get government colleges as your chances are very very low. You can get a good private engineering college in your city/town or state. It depends on your JEE marks and your category as well. Fill the JOSSA admission form properly. Do the research on engineering colleges in your City/ State or Cities like Pune and Maharashtra which have some really good colleges.

It depends upon your advanced result. As now a days, NITs considers JEE Advanced.

B.Tech ECE is good because the college you've choose for engineering is good but if you are choosing integrated course from any good college then it will also be a good choice.

Yes, you can get admission in NIT for engineering but you have to cross the cut-off of this college according to the branch and also qualify JEE Mains and Advanced.

Yes, you can get NIT for engineering but you have to qualify JEE Mains and Advanced for the same.

You got a decent score. You will get top 10 NITs. Please provide your rank for the best suggestions. By the way, you will easily get into a good NIT. Thapar University and IIIT-Bangalore are also a very good option at this score.

Hello Keshav,
As per your marks, your chances are very slim to get NITs and good govt. colleges. Try for private colleges.
All the best.

Hello Harsha,
You have mentioned your caste but you have not mentioned if you are eligible for admission under any quota. However, don't worry. I am attaching a link that will predict college for you.
https://www.resonance.ac.in/reso/news/JEE-Main-Branch-Predictor.aspx

Hello Aditya,
It will not affect. But why gap of two years? Even in one year, you can become master of the syllabus. Your academic record will surely be scrutinised and you should have answers for your breaks. That's all.