A lot of them will consider it a good (if early) deadheading and come back, if it's not cut all the way down and there are a few leaves left. What did you have growing?
I don't know. I bought a huge amount of a varied seed mix and threw it all down. Unfortunately, the plants were mowed all the way to the ground with little stalk left even.
Hard to say without knowing which flowers. I can say from experience that California Poppies, buttercups, chamomile, vetch and salvias will come back after mowing. They will be shorter though- they learn and try to avoid the mower. If you're in a zone with mild, late winters you can probably start new seeds now, if you can keep watering daily.
One of my (not literal) nightmares. This is why I told my wife I'm doing it all myself. If it takes forever, fine.
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