I have looked at your file and you seem to have laid it out correctly. Popups on the a -layer is very tricky at the moment and we have a solution coming up. Unfortunately it won't help you right now. The problem I can see is that the text underneath the tabs won't be possible to view as the popups will stack on top of eachother hiding the one you actually want to see.
My advice would be to either rethink the design so the popups aren't stacking on top of each other or actually building the whole thing using html. This could easily be done using for example hype. If you are going to use popups in the plugin I would recommend using the b-layers as it is much easier to handle but at the moment it won't solve the problem you are having with the stacking.
So, unfortunately I have no definitive answer as what you are trying to do is not really possible yet just using the plugin. As I said I would probably use html for what you are looking to do.
Concerning the html being on top of the object. At the moment this is not possible unless you are working on the b-layer, then it will layer on top.
Popups within popups is not possible yet.