>> Currently I'm developing a patch (attached below) that allows to type
>> ‘M-0 RET’ on a completion to insert it to the minibuffer, and quit the window
>> without exiting the minibuffer.
>
> Below is a better patch.  It binds C-RET to insert the completion to the minibuffer.
>
> Regarding whether to quit the window or not, this question is currently
> discussed on emacs-devel.

This is a copy of the patch from emacs-devel.
It adds two new arguments to 'choose-completion':
'no-exit' that doesn't exit the minibuffer and
'no-quit' that doesn't quit the completions window.