This article mentions that Azure Search can be used if you use Sitecore Azure Paas. But I don't see any reason why you couldn't use Azure Search with a standalone Sitecore solution. Do you really need to run Sitecore as a Paas to be able to use Azure Search?
You can use Azure Search in an IaaS or on-prem setting. You have to use the Azure Portal to manually provision Azure Search; vs. using Azure Marketplace or Sitecore ARM Templates in a PaaS setting.
There's a webinar on this topic in the Sitecore Global Virtual Summit. http://vshow.on24.com/vshow/SitecoreGVS/lobby/14168
Nope. The document is slightly misleading - I believe what it means to say is; that if you use Sitecore Azure PaaS, you need to use Azure Search (or SOLR); Lucene will not work.
I don't see any reason what so ever, that Azure Search should not be supported in an on-premise installation; be mindful of the potential performance impact however.