I cannot find an Audiobook tab located in the iBooks Store.

They are still bought via iTunes store. If you go to, for example, the music homepage in the store and click on Music above the text links/Quick Links on the right-hand side of the store you should get a popup with one option being Audiobooks e.g.

On an iOS device running iOS 8.4 there should be a Books / Audiobooks option at the top middle of the screen

I had the same problem, so good to see that still works.

But here's a question... Why can I not access audiobooks already purchased, via the new system. And why can I not find the audiobooks I have synced on my phone? I'm completely mystified by this new change. Seems to me its change for its own sake. And I do not like it, because right now I cannot see how its even logical..

Oh never mind. After I updated *everything* (OSX, iTUnes and iOS) it all worked as it should