You will need FTP access to your root. If you do not have an .htaccess file, then you can create a text file, upload and then remove the .txt. Use Notepad or a similar application. If there is a file, be careful not to overwrite anything that is already there.

Create a new line that reads, for each page, and optionally use comments to keep track of your code

301 redirects

redirect 301 /old-category-page/ http://www.yourdomain.com/new-category-page/
redirect 301 /old-category2-page/ http://www.yourdomain.com/new-category2-page/

Here's how that breaks down:
redirect 301 (the instruction that the page has moved)
/old-category-page/ (the original folder path and file name)
http://www.yourdomain.com/new-category-page/ (new path and file name)

Save and upload.

If you are unsure about FTP to the root, contact your hosting provider. Hope this helps!

Your other questions have been answered, but I'd suggest three other resources for terms:

1. Look at the impressions their site is getting in their Google Webmaster Tools account.
2. Use Bing's Keyword Research Tool - http://www.bing.com/toolbox/keywords - to get organic data and not just the paid search data from Google's AdWords tool.
3. Look at Google's Trends data - http://www.google.com/trends/ - and you'll see traffic and related keywords for those terms.

P.S. I have a client who is in a very high-end niche industry and get similar confusion from terms. BUT, they are getting impressions and traffic for terms the tools say have no traffic. The numbers are relative approximations, so keep that in mind.

Here is Jen Lopez' post on adding Facebook Insights meta tag to your website.

http://www.seomoz.org/blog/4-facebook-marketing-tactics-you-might-not-know-about

Facebook only provides space for one domain associated with each Insights tracking code.

MIke is spot on and correct! Handling 404s should be a process in which you manually map one page to another, unless you have a large enterprise site and can setup server rules to handle the redirecting process.

For you, take the old category URL, and map it to the renamed category. Do this for each and every one. After you have done that, revisit GWT, and address the remaining 404s individually.

Titan552,

The key point is that you should wrap your contact information in schema on every page in which it appears.

Twice on the contact page? It's probably not necessary, but since the search engines look at body copy differently than footer segments, I recommend using it on the body contact content as well.

Scott, admittedly you could spend hours! Keyword research can be extensive and time-consuming, so ensure you/they have a clear understanding of their target audience and local. And when you are researching keywords, take advantage of Google Keyword Tool's ability to insert the URLs of the competitors. If their competition is ranking in the SERPs, look at their keywords. One more tip... You can use SEM Rush, free version has minimum data, to see phrases for which the competition is ranking as well as which URLs.

Once you have a core set of terms that bring them value (money terms), evaluate their content to ensure they relevant content. Optimize from there.

I'd suggest getting webmaster tools accounts set up with Google and Bing ASAP.

You're on the right path!