[chamberinternet]

Can somebody help me to use If condition to hide a category thumbnails, but only if category name is called for example: LED diodes?

Open up subcategories_t.tpl (located in /skin/common_files/customer/main)

Find the following code (Around line :

    {if $subcategory.is_icon}
      <a href="home.php?cat={$subcategory.categoryid}"><img src="{get_category_image_url category=$subcategory}" alt="{$subcategory.category|escape}" width="{$subcategory.image_x}" height="{$subcategory.image_y}" /></a>
    {else}
      <img src="{$ImagesDir}/spacer.gif" alt="" width="1" height="{$subcat_img_height}" />
    {/if}

and replace it with the following:

    {if $subcategory.is_icon}
		{if $subcategory.category NEQ "LED diodes"}
      	<a href="home.php?cat={$subcategory.categoryid}"><img src="{get_category_image_url category=$subcategory}" alt="{$subcategory.category|escape}" width="{$subcategory.image_x}" height="{$subcategory.image_y}" /></a>
		{/if}
    {else}
      <img src="{$ImagesDir}/spacer.gif" alt="" width="1" height="{$subcat_img_height}" />
    {/if}

So basically, if the current subcategory is not called "LED diodes" then display the image.

Other if statement I want to use is for home page featured products. I want to rename it to New Products, but only at home page. For all other pages I wan to leave it as Featured Products. Any idea?

If it's only for the homepage then yes...
The featured products section is driven via customer/main/featured.tpl
If you make a copy of the file and call it something like featured_home.tpl and make the custom changes you want here.

Then amend customer/main/welcome.tpl (Which is the site's frontpage) to include featured_home.tpl instead of featured.tpl.

HTH