My requirement is to have category listing (with images) on homepage in with left and right arrows.
One solution is to use feature slider (that is copy home-feature.phtml to new file home-category.phtml)
here, how to add category images here. How to link home-category.phtml and images.
This is actually done in one site flipdeals.com.au.
My second query is how to stop rotation of brand images when mouse is moved on brand lists.