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I got it for Mac. What is the Wrench icon (repair) that appears over my ships. I click on it but nothing happens. How do I repair my ships? Is there a detailed explanation or manual floating around somewhere?

I'm afraid there is no manual (sorry). I do believe the little wrench thing you mention is just the status indicator saying that the crew is currently performing repairs on your ship. There is no manual action required from your part.
 
What causes crews to do repairs, I noticed that it fixes the hull (hp) aswell.

As far as I understand it, it is something the crew does on its own when the ship has taken damage.
 
The factions repair their ships at different speeds and to a different health limit but it is all automatic.

Commonwealth: Repairs at normal speed up to 50% of max health
Elite: Repairs faster up to 40% of max health
Marauders: Repairs slower to 60 % of max health

Note that the difference between faster and slower here isn't that great, but there is a difference.