Have you ever modified the source code of an open source application?

Yes - Geant4 (from CERN) and OpenFOAM for example.

I'd suppose Linux device drivers count, as does Yocto recipes and one of the main init systems (runit)...

I once wanted to modify the sources of the XED text editor because I wanted to disable 'search as you type'. It makes searching very large files impossible because as soon as you type the first character of the search string, the editor begins to mark every instance of that character. This takes ages (sometimes more than a few minutes) and while this is ongoing, it is not possible to enter any additional characters.

But to my surprise I couldn't find anything in the source code to change this. I guess it is a default of the GTK framework used to build the editor.

Yes, I maintain a few patches for FLOSS programs that are unmaintained, but still work fine after patching.
Come to think of it, I also have 1 or 2 for programs that are maintained because I don't like part of the functionality.

I had to do some hacking to make this code build. I didn't actually modify the program itself, so much as hack the make file to make it actually detect the third-party *.h files it needed to finally produce a build. IDK if that counts, since I didn't actually change the C code, just added some -I arguments to the compiler.

Hacking the build system defiantly counts. Without working build systems you'd have no FLOSS programs -- or at least none that could be built with any regularity.

Yes .. but it is an Android Application that my script automatically compiles when the upstream source changes ...

They did not ask if it was for Android, just if it was open source.
Granted, I would have used FLOSS in the question, had I worded it but I didn't write it.