Hello Sahil,

The CSAB for 2019 has been constituted with Director, National Institute of Technology, Tiruchirappalli, as its Chairperson as per the Office Memorandum of Ministry of HRD, Govt. of India that is placed at the OFFICE MEMORANDUM Link.

Based on the rank of JEE (main), admissions will also be made to the first year of Engineering/Technology and Architecture/Planning Programs on supernumerary seats in NITs for Union Territories, and in some AICTE approved Institutes for North East and Union Territories (NEUT) through this centralized seat allocation procedure.

As far as I can see on the website, there is no such word called willingness written there.

There is no such option there. If you have not secured a seat in first round then it's really very difficult to get a seat in second round. So, it depends on your luck and the choices filled by you. 

Hope your doubt is cleared.