Sharing the same templates by importing PHP files: Where should I store those PHP files? I want to be able to just edit standard PHP files which are then imported into many themes. 

I feel like a module is an overkill, so I'm happy with just a folder of files.
Your question states &quot;I feel like a module is an overkill&quot;, but (according to your own comment) the Domain ThemeKey module works perfectly for your use-case along with importing php files.
Some details about this module (from its project page):

Integration of Domain Access and ThemeKey.
Module provides additional ThemeKey properties:

domain:site_name - returns current domain's site name
domain:id - returns current domain's id
domain:machine_name - returns current domain's machine name
domain:is_default - returns true if current domain configured as default domain
domain:is_alias - returns true if system:host is an alias for current domain