I don't think its a bug - with your 1st query you searched for 2 values ored together:
1) the word "test"
2) all words (by specifying the asterix) - so any word will be highlighted

If you want to search for all word starting with test use "test*" with no space between test and asterix

The point was that e.g. the character ':' ist displayed as " & # 5 8; " (see screenshot) and i thought that it's unintended to highlight every word.

The entity display is clearly wrong. How in the world did dots get escaped?

Highlighting every word is also pointless. If * indeed searches for anything, the entire search query should simply be dropped as a restriction.

I just checked on my board - same result, but an extra hint: "*" was ignored, but seems to be used for highlighting:
search.php

// define some vars for urls
$hilit = implode('|', explode(' ', preg_replace('#\s+#u', ' ', str_replace(array('+', '-', '|', '(', ')', '"'), ' ', $keywords))));
// Do not allow only wildcard being used for hilight
$hilit = (strspn($hilit, '*') === strlen($hilit)) ? '' : $hilit;

Checking is done for single asterix, but seem not working correctly.

Maybe ignored words (eg. to short) have to be remove from $keywords - string?

I have the feeling that the entity display is not properly fixable. We use input encoding, then the BBcode parser and then search on the result. What we actually want to do is search on the plaintext. At least for MySQL fulltext this is a problem, but I've been able to reproduce the entity display with both, native and mysql_fulltext.

the "asterix"-problem is the same as here: http://tracker.phpbb.com/browse/PHPBB3-10342 ?

Now that phpBB 3.0.13 has been released, I upgraded our forum and discovered this fix breaks the ability to do any wildcard searches, i.e. "test*" will return with "You must specify at least one word to search for. Each word must consist of at least 3 characters and must not contain more than 14 characters excluding wildcards." See https://tracker.phpbb.com/browse/PHPBB3-12933 for the phpBB 3.1.2 version of this problem.

Opened new bug, PHPBB3-13548 to track.