For category url by category ID:
<?php echo Mage::getModel("catalog/category")->load(5)->getUrl() ?>
To load products of a specific category:
<?php
$cat_id = 8; // set desired category id$category = Mage::getModel('catalog/category')->load($cat_id);$products = $category->getProductCollection()->addCategoryFilter($category)->addAttributeToSelect('*');?>
<?php foreach ( $products as $_product ): ?>
<a href="<?php echo $_product->getProductUrl() ?>"><img src="<?php echo $this->helper('catalog/image')->init($_product, 'small_image')->resize(135, 135); ?>" width="135" height="135" title="<?php echo $_product->getName() ?>" alt="<?php echo $_product->getName() ?>" /></a>
<?php endforeach; ?>