With “doesn’t change a lot”, do you mean no change at all? Or can you access now at least some drive (like internal or external storage).
Basically it should work if the corrupted file gets fixed.
Well, if you can’t get apps running, maybe installing busy box won’t work either. At least the busy box app which I am using is rather an installer that - when opening the app - downloads the necessary components (binary).
For an adb install you basically need to download the apk file to your computer, and with the command “adb install FILENAME” you can install it. Though I am not sure if that will work if you cannot get root access for the adb.
I think if everything fails then you still have a chance to get a running system by yourself. You could download the stock ROM and flash it from the recovery, or you could ask someone who compiled the FP-OSOS if he or she could provide you with the images.