It is possible that \textcite will result in citations like Smit and John Doe, 2011 (including Does first name) because biblatex since v1.4 will fully disambiguate individual author names and name lists. Just see my example.
The Month appearing in addition to the year is actually a built-in feature of biblatex. Just use the date field instead of year, and conform to the required format. (Details may be found in section 2.3.8 of the documentation.)
For the reordering of names, I prefer the form \DeclareNameAlias{sortname}{last-first}. See Guidelines for customizing biblatex styles ("Bibliography -- order of first names and last names") for details.
\documentclass{article}
\usepackage[style=authoryear-comp,backend=biber]{biblatex}
\DeclareNameAlias{sortname}{last-first}
\begin{filecontents}{\jobname.bib}
@misc{S11x,
author = {Smit, Peter and Doe, Jane},
date = {2011},
title = {Me and Jane},
}
@misc{S11y,
author = {Smit, Peter and Doe, John},
date = {2011},
title = {Me and John},
}
@misc{S11z,
author = {Smit, Peter and McGee, Bobby},
date = {2011-05},
title = {Me and Bobby McGee},
}
\end{filecontents}
\addbibresource{\jobname.bib}
\nocite{*}
\begin{document}
\textcite{S11x}
\textcite{S11y}
\textcite{S11z}
\printbibliography
\end{document}
EDIT: Name disambiguation only works with biber as backend. Replace biber with bibtex8 in my example and see what happens. ;-)