Thanks, that solved the problem.
It is a little curious though because following suggestions I found in the forums, I turned off that purifier thing before I tried tinkering around with quizzes. As a result, in regular pages, I can do things like
<span class="multilang" lang="hu">
<p>Szöveg</p>
<ul>
<li>Első</li>
<li>Második</li>
</ul>
</span><span class="multilang" lang="en">
<p>Text</p>
<ul>
<li>First</li>
<li>Second</li>
</ul>
</span>
and it displays as it should.
Anyhow, I know now what works in any case, so thanks again for your help.
Eva