The robots.txt file tells spiders which files and folders to include or exclude from indexing.
It's a great way to keep images and/or content from appearing in the SERPs. One reason you might want to do this would be to save a ton of bandwidth.
In addition, the new standard allows webmasters to place a link to their sitemap.xml file, ensuring that any spider that visits the site can find the sitemap easily. Because it's the first file the spiders actually look for, there's no need to place a link to the sitemap elsewhere in the site, since listing it in the robots.txt file will accomplish this for you.
More on robots.txt files:
The Web Robots Pages
I'd fix the sitemap first, resubmit it and wait for the site to get indexed. If you're unable to remove links using Google Webmaster Tools, then you might want to get your site removed. Again, this is a last resort.
If you think it will work best for you, use the WordPress tool to generate a new sitemap. Unfortunately, I don't use it, so I'm not the person to ask for help with it. If the problem continues, try asking for specific help in a Wordpress focused forum or simply search for "Wordpress sitemap error no element found"
There can be some serious consequences with having your site removed from the index. Removing the site then resubmitting it would likely send up a flag that the site may have changed hands. Change too much content all at once and you're much more likely to end up waiting for weeks before Google decides the site is credible and not run by a spammer.
This process can be a nightmare. Not knowing any better, my site ended up being invisible for a month and a 1/2. That's a very long time for an ecommerce site to be without traffic.
Fix the sitemap, resubmit it to Google, Yahoo! and MSN and wait a week or two.