Exam

There are not much chances because they give admission after qualifying entrance exam. So, you cannot get admission there. You should take admission in any other college.
Good luck.

Yes, you are eligible for taking the exam. You can fill the application form. Good luck.

Admission is through counselling based on rank obtained in Lateral Entry Test (LET) conducted by Government of Kerala.

Admission in B.Tech without entrance is not possible even in management quota also. Every university and technical institutions are conducting their own entrance examinations and on the basis of the ranks achieved, they provides the admission.

With COMEDK, you can get seat in SMIVT mech. branch and civil branch and may Civil in MS Ramaiah.
If you want any better branch, then you have to work hard in 1st year and score 9 CGPA above to change to your choices branch.
And now, if you are willing to change branch and are confident enough that y

Please give me tentative list of colleges I can get with this score.

Eligibility-
A Bachelor's degree with Honours in Business Economics/ Commerce/ Business Studies/ Business Administration with a minimum overall aggregate of 50% or A Bachelor's degree in Science/ Engineering/ Arts with a minimum overall aggregate of 55 percent. Candidate could be a final year student

Yes, you can appear for NET exam after completing your Masters. You can apply for CSIR NET.

You can check the previous year's category wise cutoff's (category ranks) of these and other NITs at: https://josaa.nic.in/josaaorcrarchieve/Result/OpeningClosingRankArchieveN.aspx?Year=2017.
You would get an idea of your selection.
Best of luck.