I am applying for Z Visa and my Wife will be applying for an S1.

The problem is we are waiting for our marriage certificate to come in the mail. It is my understanding the invitation letter for my visa is only valid for 1 month from issue date - so if we don't receive the certificate soon, I'll need to go ahead on my own to meet timelines required by my employer.
So my questions are
1.) Am I right that it will be smoother to apply for Z & S1 together?
2.) If she ends up applying separately, will I need my temporary residence permit before I can bring her over? Or will a copy of my Z application still be sufficient? If I do have to wait for temp residency how long (ballpark) will it take before I am at the stage where she can come over?