Most of these services have public documentation about how they work in terms of network oriented APIs, or failing that some sort of SDK whose structure will typically be representative of the network traffic. For example this is what Dropbox say https://www.dropbox.com/developers/core/api

You can reverse engineer protocols for the purposes of interoperability in Europe. However there are various fine print details that matter and changes in the last few years. The wikipedia page has a summary and references to the legislation http://en.wikipedia.org/wiki/Reverse_engineering#European_Un...

However if those services have been written correctly they will be using SSL and you shouldn't be able to see what is going on with network sniffers (other than DNS names and traffic analysis).

That means reverse engineering the software which is hard and time consuming (eg you need to know assembly and using debuggers at that level). Some like Skype use anti-reverse engineering techniques. Tools like IDA help as a starting point.

However chances are that all that software you downloaded had some sort of click agreement that you agreed to saying you won't reverse engineer the software. That adds another layer of legal issues you need to address.