Filtering Post Format within category links

I have several categories, and within each of them I’m using several post formats (image, link, etc).

I’d like to have a selection of filter buttons appear when a visitor goes onto one of the category pages – so that if you’re looking at the Journal category, you’ll have the option of viewing only the images / links included in that category.

So I have two questions, which I can’t find answers to after extensive Googling:

– How can I only get the buttons to appear if there are multiple formats – how can I check if a category includes multiple post formats?
– How do I find the links to the post formats while also keeping them filtered by category (ie. not simply /type/*format* )?

Many thanks for your help!