Some shared groups not visible (event to company admin)

Hello!

We are have some problems managing contacts, groups and computers.
1. I am corporate admin and I cannot add myself to a shared group 
    (I assume admins have this permission by default).
2. There is a group (shared). There is a user with "Full Control" Permission already on
     the contact list.
     User cannot see this group on his mobile device (he is logged in with same account).
3. Another group (shared). I want to add an existing user with "Read only" permissions.
    User is not listed in a drop down list, so I can't select new user.

What do yo usuggest?

Regards,
Damjan