(Sorry for late response, we missed the notification)
Hi kippawawa,
1) You should be able to install newest APK over the existing installation and keeping your current profile (application data), no need to uninstall.
2) There is a Download button on Custom songs tab in the latest version (3.3) with several custom songs from our server. You can also visit 3rd party servers with songs for other rhythm games, e.g. we support Beat Saber format so you can visit community website such as BSaber.com and download any songs you like. You can then either copy them manually to your quest (see instructions http://songbeater.com/custom.html) or use built-in feature in SideQuest, which can download and extract ZIP file with the song for you.
3) Can you check your game settings, option No fail on Game tab? If it's ON, then the score is not written to leaderboard. If it's OFF, it should work.
4) You need full combo and also hardest and most precise hits (combo is multiplied by it). You can turn ON score per hit in % text to be sure you are achieving 90+ % in each hit. Also there might be several cases of songs/difficulty levels, which were later adjusted.
3+4) If you can be more specific we can check it out, let us know at info@songbeater.com, thanks :)