In DOM parser is used at server side in php using domxml.
While in AUX parser is used at client side in javascript

XML is a project of the World Wide Web Consortium (W3C), and the development of the specification is supervised by an XML Working Group. XML is a public format: it is not a proprietary development of any company, although the membership of the WG and the SIG represented companies as well as research and academic institutions

  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). 

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.

No. XMLHttpRequest is only part of the Ajax equation. XMLHttpRequest is the technical component that makes the asynchronous server communication possible; Ajax is our name for the overall approach described in the article, which relies not only on XMLHttpRequest, but on CSS, DOM, and other technologies.

DOM it is a hierarchical model that allows developers to manipulate XML documents easily.ie maintained by the W3C DOM Workgroup that defines an application independent mechanism to access, parse, or update XML data.