Here is a solution that uses the enumitem package: it has resume optional parameter and a series notion for enumerate environments. So I define a quest series, and an inform series, that are formatted so that the inform series leftmargin is exactly where labels of the quest series begin.
The information could be made of several paragraphs. I don't know if you want those after the first one to be indented. In my code they are; if you do not want this indentation, just remove listparindent=\parindent.
\documentclass{book}
\usepackage[utf8]{inputenc}
\usepackage{lipsum}
\usepackage{enumitem}
\begin{document}
\section*{Exercises}
Here are some exercises. Here are some exercises. Here are some exercises. Here are some exercises. Here are some exercises.
\begin{enumerate}[labelindent =\parindent, align = left, labelwidth =1em, leftmargin =! , labelsep =0.2 em, series = quest]
\item This is the first exercise. Quite a very very long exercise, with many questions and many more subquestions.
\item This is the second exercise.
\end{enumerate}
\begin{enumerate}[series = inform, leftmargin =\parindent, labelwidth =0pt, listparindent = \parindent]
\item[] Here is some information to answer the questions below. This paragraph
is indented just as much as the numbers in the list are.
Here is another information to answer the questions below. This paragraph is indented just as much as the numbers in the list are.
\end{enumerate}
\begin{enumerate}[resume* = quest]%
\item This is the third exercise.
\item This is the fourth exercise.
\end{enumerate}
\begin{enumerate}[resume*= inform]
\item[] Here is some more information to answer further questions below. This paragraph
is indented just as much as the numbers in the list are.
\end{enumerate}
\end{document}

\hspaceto shift it to the right place, but I'd really like to know of a better way. – vedadh Jul 03 '14 at 13:07