Hello,
New Registrations has been closed for AIIMS PG. The option of Final registration for completion of other details will be available for already registered candidates till 15.10.2018 for filling the Qualification, City Choices, Payment.
You can complete your registration through the official website and if you are still facing

You must have completed mBBS degree with atleast 55%aggregate marks and from recognised Institute as apprived by MCI. Secondly you must have completed 1 year rotary in ternship to be eligible.

https://medicine.careers360.com/articles/aiims-pg-eligibility-criteria

Yes you will be eligible.

Syllabus for AIIMS PG exam for MDS below.

https://www.aiims.edu/aiims/academic/aiims-syllabus/Syllabus%2520-%2520md%2520ms%2520mds%2520mha.pdf&ved=2ahUKEwjowYOc4OTdAhUSbo8KHdgsA4cQFjABegQIBxAB&usg=AOvVaw3xkLtMpLr2YW8XZLDC6LvE

Exam is conducted twice year in January and July with total of 200 MCQ and 3hours duration. Has negative marking of 0.333.

For entire exam pattern you may check bekow with eligibility criteria and expected dates. 

https://medicine.careers360.com/articles/aiims-pg-exam-pattern

Yes, you are eligbile as long as you have have obtained a minimum of 55% aggregate in MBBS ( the candidates from SC/ST category must secure an aggregate of 50%.)
It is essential that all the candidates complete the compulsory one-year rotatory internship before the deadline and are required to

Yes if you complete 12month rotary internship before 30th January 2019 then you shall be surely eligible provided you also meet other cruterias as described below.

https://medicine.careers360.com/articles/aiims-pg-eligibility-criteria

National Board of Examinations (NBE) is the conducting body of NEET PG Entrance Exam and All India Institute of Medical Sciences (AIIMS), New Delhi is the conducting body of AIIMS PG.

Good Luck!