I do , I know it does feel weird, but after all we're talking about a device you carry in your pocket and would defend with your life , so I just type "root" and do what I have to do.

Note that you cannot use "su" because it's not suid, and you cannot make su suid because su is actually a link to busybox and *you don't want to make busybox suid*.

BTW you have "user ALL=(ALL) NOPASSWD: ALL" in your /etc/sudoers immediately after the last line coming from 01sudo. Would you mind showing a listing of your /etc/sudoers.d/*

That line (which I don't have) conflicts with "user ALL=(ALL) PASSWD:" (which as peterleinchen said should be "user ALL=(ALL) PASSWORD: ALL" but I don't speak sudoer!

I just looked in "update-sudoers" and it used "visudo -c" to check the file (this is what caused dpkg to fail in your case). So I'd suggest you run, manually, "update-sudoers" and see what it spits.