If you have Capslock set to change your keyboard language, and your computer locks with Capslock enabled, you literally can't type lowercase letters of your password. Capslock doesn't work, shift doesn't make it go lowercase - you literally just have to reboot to get back in.
Yes
How would your computer lock with capslock enabled? I.e. if capslock on that computer is set to change keyboard language?
I.e. configure the custom binding to also work on lock screen. Karabiner supports this I think.
Alternatively, rebind caps lock with a custom binding and not os settings (i.e. don’t rebind keys in both a custom tool and the OS). Then, if custom bindings don’t work on lock screen, you get the default, working keyboard on lock screen.