Is there any way to change the user information through the API? Can you change the user passwords through the API?
You can use the CommunityServer.Components.User class to edit the properties of the user. There is the User.Password property and User.ResetPassword() method.
Is there any way to make the Forum module more content oriented, for instance break down posts into content items viewable/editable from within Sitecore?
The Content of the Forum module is contained in the Forum module database. You can manage Forum module Permissions for the forums.
Does the API have methods to retrieve the forum information such as the list of all of the messages in the forum or users/messages posted by a certain user?
Please use the classes from the CommunityServer.Discussions.Components namespace of the CommunityServer.Discussions.dll assembly.