If you need to work right now, you need to apply for PGWP. If you don't, you can apply for BOWP if you passed a completeness check stage in your PR application.
You wont't need a birth certificate.
Just in the following cases:
Copy of birth certificate or other equivalent document
Purpose
To prove the dependent children’s relationship to the parents
Document requirements
This document is required only if the applicant identifies dependent children...
You don't need to courier anything, just print it out and sign it.
And no issue dating it earlier than it was actually signed if that was what you meant.
Interesting. But most likely the application will be refused as you don't have a valid passport.
You can apply without an explanation and try to make an update afterwards when you get a new passport.
You mean a visitor status? Why would you need to covert?
If it's primary or secondary, they won't need a study permit if you have a worker status. But they need a status anyways so the kids can apply to change for a visitor status .