There are things that an organisation needs to do which imply having met a person face to face before they can do a check, details @ Visa Entitlement Verification Online for Organisations
You may be happy to provide your personal information to a potential employer by email but it will depend on the ethics of the organisation and their employee whether they would proceed.
I've already made an innitial entry to Australia for 2 weeks then come back to my country. Is there any regulations or links to show that when I need to come and stay permanently in Australia (or I only need to come ASAP)? Do I need to inform DIAC that I already made an innital entry to Australia?
Immi will know that you have entered, or at least your entry is in the computer and so that means your visa is validated and now you have up to five years from date of grant in which to return if it is a PR visa you were granted.