sudo hangs before password

That's interesting, it is not happening here. Works as expected, very fast. Try creating a new account or using the Guest account and open a Terminal session and test.

Already tried new accounts AS NOTED ALREADY. Please study all the notes I already show above.

I've already spent an hour with /etc/sudoers. I'll study the one above, but I found no solution using /etc/sudoers, and one has to tread carefully in modifying security files

Much more comfortable with a diff.

What change made it work, exactly?

I made my sudo command working again by commenting out following line in /etc/sudoers:

%users ALL=(ALL) NOPASSWD: ALL

@ Lloyd Chambers: Did you update your bugreport at Apple with your latest findings?

This worked out for me.

I suggest anyway to create a copy of /etc/sudoers before to try the new configuration.

confirmed!

vagrant messed up the sudoers.

This worked for me!