Can I somehow assign a reminder date (or even better also a time, if needed) so that DirOpus will remind me with a popup or with a tab that lists the reminder files that I have to deal with the file (for example invoice?)
Or is it possible to create a custom column "due" and search / filter for that somehow?
For pop-up reminders, you're best off using a reminder tool, as that isn't something Opus is designed around.
If the tool lets you create reminders via a command line or scripting interface, you could have a button or context menu in Opus which tells it to create a reminder for a given file.
Could be done using scripting. Probably not a huge amount of script code would be needed, but not a trivial amount either.