Depends on which country you are in and which project you are on. In Australia there will likely be a National Police Check, if on a government project you'll also need to do additional checks for your security clearance.
I recall they did a health check, not a background check that I am aware of.
No need to
Full Police and reference checks required
Yes, does complete background verification of the candidate.
Police Verification which is performed via Passport check,
Previous employer background check
Depending on the contract you may require a National Police Check