I'm back in my home country, but about to retire for the evening. I think we've identified the following issues here.
1) Windows stupidly makes local file drops into URLs because it's Windows.
Solution2) If http://qt-project.org/doc/qt-5/qurl.html#path
can be believed, "...will use forward slashes"
3) We quote quoted data.
Solution3) In MainWindow::browseInputFile, test if first character is a quote and then skip.
4) We mishandle multiple files dropped.
PossibleSolution) Disallow that.
BetterSolution) Make relevant data structures handle QStringList instead of glomming them together (badly) at ahd end of browseInputFile()
5) Apparently a drag of an output file is actually useful. (It also sounds dangerous for accidental overwrites...)
Solution5) don't subclass MainWindow::dragEnterEvent() & dropEvent() Instead subclass the specific input widget for the current code and new code (bonus points for refactoring/reusing) to set outputFileNames_ for the new output drop events.
They're approximately ordered by development cost. I think #1 and 2 combined are a one-liner plus testing.
I'll put this on my list tackle, but time's pretty scant for the next few weeks so if you're a budding Babel-head looking for a starter project, please go for it.