I'm trying to change/access mobile and managed accounts on a Mac network system. System Preferences won't give me the option to change a password of a mobile account. How can I view or change this password?
A managed / mobile account is controlled from the directory so you can't change that password unless there's some sort of integration with a tool like Apple Enterprise Connect or Nomad (https://nomad.menu) where the tool calls to the Active Directory to make the password change.
All Mac accounts have their password encrypted and obfuscated, so you'd have a hard time cracking them.
Best bet is to get your admin staff to assist you in resetting the passwords or letting you be the administator of this Mac and set up local accounts.