You can send Messages to other users by tapping on the Photo Credit section of a Photo. You will be presented with an option to Mention or to Send Message. This is currently the only way to compose a new Message to a specific user.
To Reply to a message from the Inbox, swipe on a message to the left and you will be presented with 3 options: Flag/Unflag, Reply, Delete. Tap reply to open the Message Composer.
To Reply from the Message Viewer, tap on the Arrow icon at the bottom of the screen on the tool bar.