Hookpad uses 3-note voicing for 7th chords and other extended chords, so the Harmony track will only have 3 notes, regardless of what chord it is.
E.g., for a root position 7th chord, Hookpad voices the 3rd, 5th, and 7th in the harmony, and the 1st is voiced in the bass. For a 1st inversion 7th chord, Hookpad voices the 1st, 5th, and 7th in the harmony, and the 3rd is voiced in the bass. If you prefer to have all 4 notes in the same register in your MIDI output, you can try voicing the bass up an octave in the mix tool.
Exporting harmony tracks with fully voiced chords is something that we could possibly implement if there was interest. We currently use 3-note voicing because it sounds cleaner in Hookpad playback.
Regarding Safari, can you verify that your Adobe flash player is up to date (we’ve had problems with safari and slightly out of date flash player). Hooktheory is slowly moving away from flash (which has given us a lot of headache), but for now, we appreciate your patience.
I really hope you implement this. I think it should totally be there. Exporting 4-note chords drives me crazy a lot of the time. The exported tracks (bass, harmony, etc.) should have an option to be 100% independent from one another.