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.

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)

XnViewMP (of all platforms) may be what you want. Although I find it for a image viewer, it works fine as a file manager, resembling the classic Windows File Manager. Configure the layout as you wish.