Considering that mashup is like a web page, I should say no for your question. But not sure if you did mean create a mashup even using qlik sense desktop. So, if you want to create a mashup (web page connecting your qvf files) I would say yes. Take a look into this:
Not exactly sure what you mean. Mashups and (visualization) extensions both use the same packaging and loading, which is available (with some small differences) both in Desktop and server, mainly to make it possible to develop both mashups and extensions on your desktop and then deploy it to the server.
So you can build a mashup and use as an extension to the Qlik Sense desktop product. That is very useful for tools, in many cases a better alternative than building a visualization extension.
Both use a qext file, where the type field is different ('mashup' for mashups, 'visualization' for visualizations). Only type 'visualization' can be added to a sheet.
So you cannot add a mashup to a sheet.