Finally I got the SharePoint Manager 2013 Online app on the SharePoint App Store after 5 very long weeks. The app was already ready back in January but due to an internal error in the approval process that resulted in a exceptional long approval time and then it was denied approval a couple of times because it did not meet all the requirements.
Question: Will the Online version cost anything?
Answer: The Online version is a per person license, but it supports a 15 days trail.
Question: What are the status of the server side version found on Codplex?
Answer: The server side version of SharePoint Manager 2013 is still under GPL and free, there will be no changes here. The development of this version will continue when needed.
From the description of the Online version: