1) Is there a pre-existing XML grammar/format/DTD that's suitable for
marking up research papers (I plan to write several)?

2) If so, are there any pre-existing stylesheets I could use to
transform them to MLA or APA (or other) styles in XHTML, Microsoft
Word, or Adobe Acrobat formats?  (For example, displaying the
citations appropriately for each style, so I don't have to concern
myself with mundane details like that)?

Please check these sites

XML.org, Focus Areas provide domain-specific content on XML standards at
http://www.xml.org/

Commerce XML at http://www.cxml.org

ebXML - Enabling A Global Electronic Market at http://www.ebxml.org/

The CoverPages at http://www.oasis-open.org/cover/sgml-xml.html

XML Files - Extensible Markup Language at http://www.xmlfiles.com/

For more XML sites please check,
http://search.dmoz.org/cgi-bin/search?search=xml

Regards.