Peter has a great answer with some good resources referenced, and i'll try to add on a little bit:
1. Why it is important that the rel canonical tag points to a non-parameter URL?
It's important to use clean URLs so search engines can understand the site structure (like Peter mentioned), which will help reduce the potential for index bloat and ranking issues. The more pages out there containing the same content (ie duplicate content), the harder it will be for search engines to determine which is the best page to show in search results. While there is no "duplicate content penalty" there could be a self inflicted wound by providing too many similar options. The canonical tag is supposed to be a level of control for you to tell Google which page is the most appropriate version. In this case it should be the clean URL since that will be where you want people to start. Users can customize from there using faceted navigation or custom options.
2. What is the extent of the negative impact from having rel canonicals pointing to URLs including parameters?
Basically duplicate content and indexing issues. Both of those things you really want to avoid when running an eComm shop since that will make your pages compete with each other for ranking. That could cost ranking, visits, and revenue if implemented wrong.
3. Any advice for correcting this?
Fix the canonical tags on the site would be your first step. Next you would want to exclude those parameters in the parameter handling section of Google Search Console. That will help by telling Google to ignore URLs with the elements you add in that section. It's another step to getting clean URLs showing up in search results.
I tried getting to http://www.chasing-fireflies.com/costumes-dress-up/mens-costumes/ and realize the parameters are showing up by default like: http://www.chasing-fireflies.com/costumes-dress-up/mens-costumes/#w=*&af=cat2:costumedressup_menscostumes%20cat1:costumedressup%20pagetype:products
Are the parameters needed for every URL? Seems like this is a websphere commerce setup kind of thing.