How to remove the word "New" for the new comments
copy /modules/comment/comment.tpl.php to your theme folder e.g. sites/all/themes/mytheme/(templates/)comment.tpl.php.

That theme file will override the comment.tpl.php from core, in that file you can remove this block:

&lt;?php if ($new): ?&gt;
  &lt;span class="new"&gt;&lt;?php print $new ?&gt;&lt;/span&gt;
&lt;?php endif; ?&gt;


This way is perfectly fine, you are not changing/ hacking core. The theme system was meant to be used that way :)