Environment with first paragraph in bold and no pagebreaks

Question

I would like to setup a new environment which typesets the first paragraph in boldface, the following paragraphs in normal text, and with (possibly) no pagebreaks between the first paragraph and the remaining text. How can I do?

For example, something like the following:

\begin{question_and_answer}
This is a question, which should be highlited in bold 
(or by changing font, or by another method) and preceded by a progressive number.

This is the answer, in normal font.

The answer is composed by one or more paragraph. There shouldn't be a 
pagebreak between the first paragraph and the second.
\end{question_and_answer}

Or maybe something like this:

\begin{question}
This is the question, as the previous example
\end{question}
% no pagebreak here
\begin{answer}
This is the answer, as the previous example
\end{answer}

Answer 1

If your paragraphs have only normal text, you can define

\newenvironment{highlightnobreak}
  {\par\bfseries
   \def\par{\widowpenalty=10000 \endgraf\penalty10000 }}
  {\par}

Use it like

... some text before.

\begin{highlightnobreak}
The first paragraph here will be typeset in bold face.
\end{highlightnobreak}

And this text, which is in the paragraph following the
environment will be in normal type.

The highlighted paragraph will never end along with a page and will be always accompanied by at least one line of the following paragraph on a page. A page break can however happen before the second-to-last line of the highlighted paragraph.

More customization is possible. For example, a vertical space after the highlighted paragraph can be inserted modifying the definition into

\newenvironment{highlightnobreak}
  {\par\bfseries
   \def\par{\widowpenalty=10000 \endgraf\penalty10000 \medskip}}
  {\par}

We can improve it with a progressive number and also a vertical space before it, to match the one after:

\newcounter{highlightpar}
\newenvironment{highlightnobreak}
  {\medskip\par
   \def\par{\widowpenalty=10000 \endgraf\penalty10000 \medskip}%
   \stepcounter{highlightpar}\bfseries\thehighligthpar. \ignorespaces}
  {\par}

TeXnical note

It's important that the \par that closes the environment does more things than usual: here we order it to set \widowpenalty to a no-break-before-the-last-line value, then to finish off the paragraph and to tell TeX no-pagebreak-here.

The relevant items TeX will see are then

〈last line of the highlighed paragraph〉
〈penalty 10000〉
〈\medskipamount glue〉
〈\parskip glue〉
〈\baselineskip glue〉
〈first line of the following paragraph〉

so that, by rule, it will not break pages at any of the glue items, because they are not preceded by nondiscardable items. Only the penalty would be a feasible page break point, but it's "infinitely big" and so TeX won't consider it.

Answer 2

You can redefine \par locally to reset the font and use \@par which resets \par to its normal definition. I added the penalties given by egreg as well which should avoid a pagebreak right between the two paragraphs. If you want to have no page break at all in all included paragraphs than you can wrap the whole thing in a minipage.

\documentclass{article}

\makeatletter
\newenvironment{myblock}{%
    \par\bfseries
    \def\par{%
        \widowpenalty=10000
        \@par\normalfont
        \penalty10000
    }%
}{%
    \par
}
\makeatother

\begin{document}

\begin{myblock}
    text text text text
    text text text text
    text text text text
    text text text text

    further text further text
    further text further text
    further text further text
    further text further text

    further text further text
    further text further text
    further text further text
    further text further text
\end{myblock}

\end{document}