At this point our Salesforce IDE is focused on the development aspect. We do not yet offer a graphical interface to run deployments between multiple orgs and environments. This is on the roadmap, but we cannot provide you with a target date on when this would become available.
There are two way to deploy in the meantime:
You can run the Force.com Migration Tool from the terminal. Your workspace is running on a full Ubuntu Linux VM and all the Salesforce objects are synchronized as files which can be used with other utilities.
You can connect multiple Salesforce environments to the same Cloud9 user. Each of them will be available as a separate workspace. To synchronize between the workspaces, you can use Git with your Salesforce workspace.
Debug logs are not visible in the IDE but you can see them in the Salesforce Developer Console. To go there quickly, choose Salesforce > Force.com > Developer Console in the menu bar. This will automatically log you into the correct Salesforce account and open the console where you can open your logs.