Yes, a piece of paper or a sheet of paper can be a document. A document can also be many pages if you are talking about a document that is on a computer. Often a document that you have stored on a computer will be called a document even if it is hundreds of pages in length. If you are not referring to a computer document, a document will be one page - sometimes two or three pages, but not often. Sheet of paper is spelled with two "e"s. The way you spelled it is an offensive word meaning feces.

I would say that any written material can be called a document. Generally electronic files are called document files or just documents (e.g., a Word document) or just files (e.g., an Excel file). A shit of paper would come out your butt hole--a messy affair. Best to use sheets of paper instead. ;)