There is no general API to let you write or edit Google+ posts that appear directly on the stream. The general philosophy behind the Google+ API is that anything posted must be done with an explicit user action. So while you can prompt the user to post from your app, the user must actually post it themselves.
Similarly, while you can create a app activity that will post on the user's profile without explicit user action, the user still has to take actions to make that visible. App activities are only visible to a limited group, and are not posted directly to the user's stream. To place it on the stream, the owner must explicitly share it. (App activities are meant for event-like actions, such as watching a movie or checking in at a location.)
Accounts that are part of a Google App Domain (ie - not gmail accounts) have this lifted slightly. Applications can automatically create a post with visibility limited to other members of the organization.