[pc]

So inside {foreach} statement for listings like this

{foreach from=$galleries var=$gallery counter=$counter} ...

on category pages or any other pages just paste this:

{if $gallery.date_added > time() - 604800} New {/if}

where:
$gallery.date_added The date and time that the gallery was added to the database
$gallery.date_approved The date and time that the gallery was approved
$gallery.date_displayed The date and time that the gallery was selected for display

and for the index page I'm not sure if this will work but try to play with something like this:

pull all categories from db:

{categories var=$categories order=name}

{assign var=$startswith value='ZZ'}
{foreach var=$c from=$categories counter=$counter}
{if $c.name[0] != $startswith}
{assign var=$startswith value=$c.name[0]}
<b>{$c.name[0]|htmlspecialchars}</b>

{/if}
<a href="{$c.page_url|htmlspecialchars}">{$c.name|htmlspecialchars}</a>

now insert here foreach code for pulling galleries from one category that you have on your category pages and instead of url , keywords and description just add this inside foreach 
{if $gallery.date_added > time() - 604800} New {/if}

{/foreach}

I dont have my tgpx installed but from what I remember it was something like this.