I have never used phpbb within a s9y site myself. I would assume that our plugin does not limit functionality, but in general, we try to recommend to keep "extra stuff" like guestbooks, forums etc. that do not really provide blog functionality separate. (Since we have opted to develop s9y first and foremost as a blog system, not a CMS.)
I assume people that actually use the phpbb integration could say more about this, though.
There is no dedicated ZenCart plugin, so it depends on what ZenCart "needs" to be integrated. (I have never used ZenCart, so I don't know.)
You can (and should) use the static pages plugin for that but can also use static HTML alongside s9y if you wish.
Not sure what you mean by that. Do you mean if blog posts can be published automagically at some point in the future? (Yes.) Do you mean if one editor can write a post but has to wait for another (higher-level) editor to publish said post? (Yes.)
The Serendipity website is a complex beast which consists of multiple systems.
blog.s9y.org is powered by s9y, the forums are powered by phpBB. Plugins and themes are generated by some magical PHP script that Garvin once built himself, and the rest of it is generated from markdown by Jekyll through GitHub pages. (That part used to be a wiki, but I forgot what wiki it used. Everyone hated it, though.)
To complete that, all of the s9y source code including plugins and themes is hosted on GitHub.
Yes, if your webserver supports on of the techniques required to generate them (usually that means Apache mod_rewrite). It may depend on what exactly you mean by "search engine friendly", but there are also ways to customize URL( schema)s to some extent.