Positioning logo in the front page as well as slides

Question 1: You can use any of the fields given by \author, \title, \date, or \instituteto place the image in the title page; if none of those fields allow you to achieve the desired placement, you can use the textpos package. The example below uses the \author field to add the image.

Question 2: With the help of the textpos package you can add the logo to the frametitletemplate using \addtobeamertemplate.

A simple example code:

\documentclass{beamer}
\usetheme{Madrid}
\usecolortheme{beaver}
\usepackage{textpos}
\title{The title}
\author[The author]{\includegraphics[height=1cm,width=2cm]{cat}\\The Author}
\institute[Inst.]{The Institute}
\date{\today}
\begin{document}
\begin{frame}
\maketitle
\end{frame}
\addtobeamertemplate{frametitle}{}{%
\begin{textblock*}{100mm}(.85\textwidth,-1cm)
\includegraphics[height=1cm,width=2cm]{cat}
\end{textblock*}}
\begin{frame}{Motivation}
Now the logo is visible\end{frame}
\end{document}