Numbering equations like 1a and 1b

use align end subequations instead of eqnarray or equation

\begin{subequations}
    \begin{align}
        p(w) &\sim \mathcal{N}(0, Q)\\
        p(v) &\sim \mathcal{N}(0, R)
    \end{align}
\end{subequations}

 See here.

Making list / glossary of acronyms and abbreviations

The easiest way to write abbreviations is to make use of the acronym package, see
http://latexbestpractice.blogspot.pt/2013/08/writing-acronyms-and-abbreviations-in.html

To define the glossary (list of abbreviations), I define acronyms using
\acro{short}[short-to-appear]{full-definition} command. Then referring the abbreviations with \ac command. Note \acf, is for full description, even if it's not the first occurrence, and \acs for plural form.

\usepackage{acronym}

...

\subsection*{Abbreviations}
\begin{acronym}
    \acro{mse}[MSE]{Mean Squared Error}
    \acro{mmse}[MMSE]{Minimum Mean Squared Error}
    \acro{}[ODE]{Ordinary Differential Equation}
\end{acronym}

...
\ac{ode} ...
\ac{mse} ....
\acf{ode}