Exam

Yes, you will definitely get the CSE group in Gayathri Vidhya Parishadh. Moreover, you also get Sri Venkateswara University Tirupati.

If no rank has been assigned to you in the EAMCET, you did not qualify. However, you can use your JEE rank to check for colleges to which you qualify. JEE Mains 2018 College Predictor
Use your JEE Mains 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges

Indian Maritime University (IMU) conducts IMUCET (Common Entrance Test) for admissions various programmes offered by IMU campuses and its affiliated institutes. Please refer to the link provided below for a detailed list of courses which you can pursue via the IMUCET exam:
https://www.shiksha.com/uni

Hello,
If you are preparing for the UGC NET Economics Exam first of all you need to complete the Post Graduation from Economics from the recognised University with atleast 55 % marks for General Category and 50 % marks for the Reserved and Female Category Students
The Tips to prepare for the UGC NET

There are very low chances of getting any government college but you should try for other colleges. And, you should also go for the state level counselling. Otherwise, you can go for the private colleges across the India. You can get a better one.

In my opinion, you should choose the branch in which you are interested as every branch is best in their field.

You have very low chances of getting an NIT as per your marks. According to your marks, you should appear for advanced exam. Chances will increase if you clear the advanced exam.