This is typically caused by a link on the page that is not formed correctly.

A quick way to check for an association in Google is to search and see what is highlighted. I chose to search for "Barnes and Noble" who reside on barnesandnoble.com and whose brand is Barnes & Noble. The answer is that no, they are not associated, but that doesn't mean that your site won't show. Obviously Barnes & Noble has established themselves as a brand and will show if you search with and or &.

Yes, you will want to redirect it. Be careful though as a lot of times this isn't done correctly and creates a loop. There are multiple ways to do this including but not limited to DirectoryIndex or a RewriteRule

Came here to say what Ray already said.

https://support.google.com/webmasters/answer/76329?hl=en

Use dashes. Underscores don't specify any specific function whereas dashes are specifically word separators.

Linda, I think the reason EMDs still work is because of their citations and links from those and branded profiles. Mostly, these type of links don't show in tools like OSE and Ahrefs. If you really look, those that have an address, and Google+ listing will have a lot more listings elsewhere because of syndication and include keyword rich titles, content on the page, etc. Those that don't have Google+ and haven't setup social and other profiles or have NAP listings typically rank poorly even if they are EMD. The other trend I've noticed is that some of these rank well for variations of their phrase (because I feel they are getting special treatment as a brand) but for something in the same niche but not included in their brand terms, they don't necessarily rank well for.

As Miriam said, check if people search for the county. In the particular area where TheeDesign is located (Raleigh, NC) we are referred to as the Triangle (Raleigh, Durham, Chapel Hill) but almost no one searches this way. The county is Wake County, but few people search by the county name either (more in some industries than others,) and typically the city is the highest search terms. So you have to debate whether the extra effort and planning is worth the extra visitors or not.

This is probably the number one question asked in the Q&A section. I think it gets answered about every week. Subfolder is preferred as subdomains can potentially be treated as a separate website. Keep them in subfolders and you'll help the entire site.

If you are going to expand further on each service, then it makes sense to break it down further and use a blurb on the main services page for each. Google what is called a silo site structure for more information.