You can achieve this scenario in the following way. Lets say you will use CMS.File for uploading the documents, first of all you need to add extra column called "extension" for this CMS.File document type and mark this column as searchable. Then whenever you will create a new document of this type, you will also fill this column with file extension, for this purpose you could use Global Events. When you have this column filled with value, you can use it as a property of Smart Search filter web part - https://docs.kentico.com/display/K81/Using+search+filters .One note, I would not recommend you to use the default CMS.File document type, you should clone this document type first.
As for your second question, I am sorry but I do not understand what exactly do you mean. Could you please describe this requirement in more detail? Thank you in advance.