There is no code for the new, featured etc badges to show on the home page sliders.
You would need to change the code in the templates/your_template/html/com_virtuemart/virtuemart/default_products.php to achieve this.
You would need to add some code like in templates/your_template/html/com_virtuemart/category/flexv2.php around line 236
The cat names are supposed to only appear on a hover - that's part of the template style - see -
www.flexiblewebdesign.com/virtuemart-2-template-fashionmart/
to have them show always you would need to add
<div class="FlexibleFrontpageProductName">
<?php // Product Name
echo JHTML::link ( JRoute::_ ( 'index.php?option=com_virtuemart&view=productdetails&virtuemart_product_id=' . $product->virtuemart_product_id . '&virtuemart_category_id=' . $product->virtuemart_category_id ), $product->product_name, array ('title' => $product->product_name ) ); ?>
</div>
outside the FlexibleFrondpage_action_hover class div and style it - also make it disappear on hover...
Cheers