You need to use
\renewcommand{\cftsectiondotsep}{\cftnodots}
in order to remove the dots for \section titles in the ToC. Or, in general,
\renewcommand{\cftKdotsep}{\cftnodots}
for the sectional unit K. For removing all dots the easiest way is to redefine the dot used to be empty: \renewcommand{\cftdot}{}. See chapter 9 Contents Lists (p 164) of the memoir documentation.
You can change \contentsname. It will still be set as a chapter though. And you would most likely use \tableofcontents* to have it removed from the ToC itself.
Here's a short minimal example highlighting the above:

\documentclass{memoir}% http://ctan.org/pkg/memoir
\renewcommand{\cftsectiondotsep}{\cftnodots}% Remove dots for section
\renewcommand{\contentsname}{}% Remove \tableofcontents' title/name
\begin{document}
\tableofcontents*
\chapter{First chapter}
\section{Section One}
\section{Section Two}
\section{Section Three}
\chapter{Last chapter}
\section{Section One}
\section{Section Two}
\section{Section Three}
\end{document}