For the "Proof that the applicant fall within critical skills..." All you need to do is download the current critical skills list, print the 1st (cover) page and the page that contains your discipline (marked with asterisk) and include wth your application.
Both my critical skill and PR
permits applications took about 3 and 3.5 months respectively. There is a special section in DHA head office that deals with critical skills and PR
(27b) permit application only.
As a fresh graduate, don't you need to apply for critical skills permit 1st?