Is there a list of all universities by country including their websites, location, latitude and longitude, facebook, twitter, youtube, founding year etc. I can't believe such a data set is not publicly available.
You can use the following query to generate the list of all universities:
You can use Wikipedia to create your own dataset. It will not be hard. Here are a few details:
Divided by continent and country, you have a list of all the universities
Then in every wikipedia page of a university, you can find as many details you want:
For example, in Aristotle University of Thessaloniki you can find coordinates, founding year, website etc.