Okay I found the issue on this BIND_ACTION() problem. (However, this doesn’t solve the original problem of the config file not updating every parameters as I explained before.)
Regarding the last problem, my function weren’t called by the binding simply because there was no “UFUNCTION()” before the function declaration in my headers. Adding this solve the problem. However that seems a bit weird, these functions are not intended to be called by any blueprint of the editor, just by a binding/the internal C++ code. Also, there was no warnings or mentions in the log to guess that.