Sudoers - group managing and reboot/shutdown

I've got a group (let's say name "group1", ID = 1234) and a user (let's say name "user1", ID="4321"). I want to do two things:

1. I want that user to change passwords from other members of that group, but only from that group.


2. I want every member of that group to be able to use reboot/poweroff commands without using their password every time.

I have read that page (http://ift.tt/pA2Vvg) but I am still not able to work out my problems. Help appreciated!

/This is a repost from Ask Ubuntu, sorry it's my first post. I am using debian./