It uses Solr 1.4. To be honest, I haven't had my finger on the Solr pulse for a year, so I missed the entire 3.x release. I'll look into 3.x ASAP and probably migrate all of my projects to the latest stable version. Their releases seem to be coming more swiftly than they used to (a year and a half between 1.4 and the next major release, 3.1, and then four incremental releases in the last eight months).
You can add additional elements into any component: scopecontent, controlaccess, and any other element that can be placed into the did. Components are loaded into their own form, which is separate than the form for editing the core of the finding aid. This is done for scalability and keeping the UI as simple as possible.
With Google Analytics, I haven't given much thought to public stats, but I will eventually integrate a Google Analytics feature into the EADitor configuration file, as I have done in another application I am working on at the American Numismatic Society which is geared specifically for coin collections (Numishare). You can copy and paste the HTML that Google provides you for the analytics into a text box in the application settings page, and this will include that code in the HTML for the public site to activate the analytics. I forgot to add this feature to EADitor before releasing the newest beta, so it will have to wait until the next release (unless you keep your application up-to-date with the subversion code).