Does Skype client in some way harm the privacy of information not submitted over it? For example, by capturing the contents of the screen, scanning the disk, the memory of the system and submitting this information anywhere. Is it safe to use Skype on government or corporate computers for unrelated activities?
Skype is definitely not a safe client to use. A Google search of "Skype exploit" will reveal a lot of its problems in regards to exploits and various news articles provide information on how the NSA uses Skype as part of its Prism program (e.g. http://arstechnica.com/tech-policy/2014/12/newly-published-nsa-documents-show-agency-could-grab-all-skype-traffic/). Note: Although the news articles do not indicate that Skype is being used as spyware targeted at the device(s) itself, this may still be a possibility so it's best to stay away from Skype.
The good news is there are safer alternatives and one example is Tox (https://tox.chat/).
Also, Open Whisper Systems (a company recommended by Edward Snowden) has apps focussed on privacy/security (https://whispersystems.org/) including a mobile messaging/phone app named Signal.