You are not limited to the style web site created by this script. You can
copy the "Create Web Site.scpt" file from ~/Library/Application Support/GEDitCOM II/System/Scripts
to the same location in your user folder (~/Library/Application Support/GEDitCOM II/Scripts)
and then edit it with Apple's Script Editor. You can change the display or content as
desired or use that script as a model for creating an entirely new web-site creation script.
For more details, see http://www.geditcom.com/tutorials/customweb.html
The last line is a link to a tutorial on how to customize the script to get whatever you want. Anything that does show not up is because the script was not written to include that information, but you can rewrite to include exactly what you want. Many of the things you mentioned are not included, but most could easily be added.
Regarding viewing on iPad. The created web site is using all standard HTML, so the only issue is if iPad supports them all. Other than that, one could write a new script to make web site customized for iPad or iPhone display, but this one is intended for desktop viewing. Such web sites usually work fine on iPads, but not always.
A. And, probably unrelated to the create a website, but I see it there too, I have several marriages which occur out of order. Is there someway to put them in order.