NIT

Your chances of getting ECE are quite low. Try for some other good private colleges.

Congratulations for securing such good mark. Your chances of getting NIT are quite high.
Please have a look at previous year's cut-off.

Just go through the JoSAA website:
www.josaa.nic.in
You will find all the related information there it is very simple process fill your choice according to the guidance and you will get the best-filled choice on the basis of vacant seats available.

If it is your first attempt and you don't want to lose your effort, then join the NIT and there you can prepare for JEE Advanced along with the college. Many of my friends have done this and all have passed with flying colours.

PLACEMENT WING:
The placements were good and companies were adequate. Many companies like Reliance Jio, L&T, L&T Infotech, National Stock Exchange Infotech and Mu Sigma had visited for placement drives and about 70 percent of the final-year students got selected. All the companies offered an average package of 3.5 Lacs per annum. Snapdeal offered 15 Lacs per annum and 2 students bagged it. I got a package of 3.5 Lacs.
5/10.

Hello,
I hope you are doing well. Don't go for a branch, go for a college. You can check the list of colleges including NITs and IIITs that you can get according to your marks and rank. Use Shiksha JEE College predictor:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor?utm_source=connect&utm_medium=CR_JEECP&utm_campaign=7489993

Yes, you can get but you have to crack the JEE Mains entrance exam.

There is a slight probability of getting into an NIT. The admission into an NIT also depends upon the home state of the candidate. Home state is the state where one did the class 11 and class 12. Please check out the following link for the opening and closing ranks in various institutes last year : https://josaa.nic.in/webinfocms/public/view.aspx?page=46. However, do not get disappointed if you don't get admission into an NIT. There are several other good institutes.
All the best!

Hello,
I hope you are doing well. No you can't give AAT examination because you didn't even clear the cutoff of JEE Advanced. The minimum criteria for getting into AAT is to clear the JEE Advanced cut-off. You should go for NITs.