Before you can reply to a customer message, you need to assign that message to yourself. Once you are alerted about an awaiting interaction in the left pane under the Ongoing folder, you can simply click on the message to accept the interaction. The interaction status will change to Ongoing case once accepted.
When replying to a message where you can answer with several accounts, there is a dropdown immediately following the From field, where you can select an account to use in the reply.