Yes, the W3C recommends using XHTML which is 'a reformulation of HTML 4 in XML 1.0'. This specification defines HTML as an XML application, and provides three DTDs corresponding to the ones defined by HTML 4.* (Strict, Transitional, and Frameset). 

TO make existing html files to xml you can convert them to conform to some new document type (with or without a DTD or Schema) and write a stylesheet to go with them; or edit them to conform to XHTML.
It is necessary to convert existing HTML files because XML does not permit end-tag minimisation (missing , etc), unquoted attribute values, and a number of other SGML shortcuts which have been normal in most HTML DTDs.

Yes, if the document type you use provides for math, and your users' browsers are capable of rendering it. The mathematics-using community has developed the MathML Recommendation at the W3C, which is a native XML application suitable for embedding in other DTDs and Schemas.