B.Tech Counselling

You have to clear cutoff for the eligibility for any state or Madhya Pradesh B.Tech counseling. No worries about attending counselling. A student did not cross cut-off mark means that he is not eligible to appear in JEE Advanced. If a student doesn't qualify, depending on his marks (after normalization), he is provided a rank, for suppose, let us consider the rank provided by you I. e.27000. With this rank, you can get a seat somewhere in an NIT (Though, not the best NIT, but just an NIT). You will be able to attend counselling and the only thing is that, you are not eligible for Advanced.

It is utmost necessary that you submit all the original documents, they won't give you your seat even if you have cleared the exam, and yes they can very well do that. If you don't have any original document don't panic, at the time of admission, you'll be given a time of 15 days to produce the document which you don't have.

For IIT, if you have qualified JEE Advance, then within the 15 days of announcement of Advance result counselling process will start. For private institution, there is no need to participate in counselling you can go direct and on the basis of your qualifying exam you can take admission. Best of luck.

No, there is no such exam. Moreover, IIT-JEE is only held only for central government run institutions across the nation.

AP-EAMCET 2018 College Predictor
Use your AP-EAMCET 2018 rank to see where you can get admission at the link provided below:
See the courses, colleges & rounds you may crack
The result is based on admissions data of AP-EAMCET 2017
Get resources & insights on colleges & courses
https://www.shiksha.com/b-tech/resources/ap-eamcet-college-predictor

You have try until 2nd Counselling, you will surely get the seat with this marks.

You have to score more than 80 % to attend the BE counselling in Madhya Pradesh (Madhya Pradesh).
Best of luck for your future.