Yeah, I'm not a big fan of mega menus or mega footers. Every link on a page dilutes the value of every other link on the page, so keep the number of links per page as low as possible, while optimizing for usability.

Links in the footer carry very little link value, so I wouldn't add top category links to the footer just for SEO purposes. Looks at it more from a design/user experience perspective. If having the links in the footer makes navigation easier, then go for it.

As with anything else, the best thing to do is to test it. Install a click tracker such a CrazyEgg or ClickTale and see how people actually navigate the site. Test having the links in the footer vs removing them, and see if it affects usability, conversions rates, or SEO performance. Then keep the links that work the best.

I would check in Moz Analytics or Google Webmaster Tools to see if there are any new 404 errors to ensure that the 301 redirects were put into place properly. It could be possible that not everything was redirected properly.

I would also look at the indexation numbers in GWT as well as run a site: search in Google, to see if any new pages have been indexed. Wordpress tends to create a lot of duplicate content pages such as category archives, tag archives, date based archives, author pages, etc. so make sure those aren't being indexed. Use a All-In-One SEO or Yoast plugins to clear those up.

Finally, go into Google Analytics and look at the landing pages that were driving the most traffic before, and compare it to after the change. You may be able to isolate a few high traffic pages that are responsible for the traffic drop.

If none of those things turns up a problem, don't panic. 4 days is not a long time and an 80% drop is not unheard of. It can take some time for Google to digest all the changes, depending on the size and authority of your site. Make sure to submit your site to be indexed in GWT under Crawl -> Fetch as Google. You can also speed up Google's crawl by building more links to your site. Twitter, Pinterest, and Google+ are all easy ways to get pages crawled and indexed, as well as getting links from high authority sites.

The question mark and the values that follow are known as "query parameters" or "query variables", and they actually can impact your SEO. Google can look at the different variations of the URL, and index them as separate pages, leading to duplicate content.

The easiest fix for this is to put a canonical tag in your header, so that Google knows the what the proper URL for the page is supposed to be. You can also tell Google to ignore specific query parameters in Google Webmaster Tools under Crawl > URL Parameters.