how to browse photos in mac folder via iPhone
The app store has some pretty good options for file browsing apps.  I use FileBrowser for example.  FileBrowser description.


  FileBrowser is the original and best file manager and viewer for iOS.
  FileBrowser can view, copy, move, upload, download, stream, and manage
  files between computers, servers, NAS drives and cloud storage in any
  direction. You don’t need to install any other software. FileBrowser
  will scan and locate computers on your network and connect in seconds
  and will connect to cloud storage quickly too.


Here's a link to FileBrowsers support guide to setting up "External Access", since thats what i'm taking your after with references to DropBox.  This takes some setup but then you can access your files on the Mac Mini without limitations of being on the same network.  

In a nutshell you are going to either open a port in your network firewall or setup a vpn to be able to get on the same network as your MacMini when outside of your home.