I use writer plus[1] which is a free Android app and writes to .md files that I sync to my computer via syncthing. Then you can use any markdown application on the desktop (there are several open source ones on Linux).
Nope, because I don't like file-based sync. It's slow, unstable and hard to implement. People will say "how about Google Drive/OneDrive/Box support?" Hell awaits you.
From a developer point of view, maybe. From a user point of view it’s a quite reliable and well known mechanism to sync between platforms. Dropbox is already what I personally use to manage my documents between all my devices, it’s part of my various workflows. I personally don’t want to add other syncing mechanisms if I can avoid as that forces me to create/manage an additional account and give my trust to an additional platform.
Of course I may be an outlier but I don’t think that’s the case, Dropbox is well established. Inkdrop looks really, really nice and I might be a user of such a tool, but only for the editing and categorizing part but if I cannot disable the syncing using your backend that’s a blocker for me.
Anyway, congrats for the work that you’ve done, I hope you will change your mind at some point :)