Welcome to the Forum.
Family reunification is not a right for non-EUs, as strange as that sounds. The authorities will be looking for a longer-term contract (i.e. not just a few months) and that she'll have sufficient income to support both of you.
No, you should not submit a separate application if you're already included on hers.
The timeline is hard to say. It takes as long as it takes. If all the paperwork is in order then I've seen 8-12 weeks as a common timeline.
From what I understand, not all non-EU dependent spouse permits allow work at the start. I think if you do find a job you can take the contract to the municipality and they can add the work permission to the permit. But I'm not 100% sure on that.