Apple - File browser with treeview

QuollEyeTree has many of these features http://binnie.id.au/QuollEyeTree.html

It was designed as a XTree/ZTreeWin implementation for OSX.

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just stumbled onto your question. I use "Easy Explore", it's on the Mac Store. It fits all your requirements -except the tab feature:

https://itunes.apple.com/us/app/easy-explore/id789939414?mt=12

you could give it a go (even has picture preview functionality)

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