I'm assuming you're using the traditional excel plugin model (written in c++ or .net) and not their new "Office Apps" (formerly add-ins) that works on both excel native and in Office365 web versions of excel?
Odd, what problems would you have hosting SQLite with an Office App? I've got a solution that could work if you're interested, it's a bit of a hack but I've done a proof of concept before that shows it works... Essentially you can run your own local web server as a service, and have the Office App make use of this service. You could even get the web server to start when Excel starts.
Depends on how you host the app. If it's hosted locally, then no.
>"and on the Mac"
Maybe. I'm nor that familiar with the Office for Mac features. I did try to search online to see whether Office for Mac supported Office Apps, but it's not the easiest thing to search for.