I poked around a bit at this and could find no way to accomplish what you want to do and nothing in the Dolphin settings that seemed to address this functionality.
I use Konqueror as a file manager (it was the KDE default before Dolphin). In Konqueror, with the sidebar enabled, you can open items on the sidebar in new tabs. You can also and remove items to the sidebar. I don't think that you can add the history to it, but you can list directories and devices. In addition, you can have multiple tabs open, but I don't think you can tile the tabs.
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