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With the redirects in place, it will sort itself out as Google crawls and switches the pages and I think you should just let them be. They are not considered duplicates in this case.
While Google has an option to remove an entire folder in GWT from their index, I think this would be bad in your case as the new structure is not indexed yet.
Under Crawl in GWT, you might want to Fetch the main category page and submit it to the index as this could speed up the transition.
Optimize the Google+ page, ensure NAP (name, address, and phone#) consistency, build NAP listings (Check out Moz Local to cover the data aggregators and Whitespark for additional opportunities,) ensure you have listings at any local directories such as city specific, BBB, chamber of commerce, and work on building any industry specific pizza links to increase their organic rankings as well. Other items such as adding schema markup to the NAP on site might help.
Under columns in Adwords, add in Impression Share to make sure you're actually showing 100% of the time.
In cases where there are multiple relevant pages, Google can show different ones. Drill down in Webmaster Tools under search queries and click one of the terms. You will see how often each page is shown as well as how often the results were returned in different positions.
331 pages returned by Screaming Frog.
Sorry, looks like the search wouldn't be causing it. I do see a lot of your crew pages are throwing a 301 redirect to screaming frog, but I can't duplicate this manually. It doesn't seem to crawl past page 9 though. Also, most of your internal links are redirecting as they include the city name in the url, and then strip the city out for the final page. I can't seem to access your robots.txt to see if something is preventing the crawling of these pages, but that might be where the problem is.
A site:icrewz.com shows 2,870 results indexed in Google.
https://www.google.com/search?sourceid=chrome-psyapi2&ion=1&espv=2&ie=UTF-8&q=site%3AiCrewz.com
However, when I try with Screaming Frog, I don't get nearly that many. Looking at the site briefly I think the problem may be that some results or pages are hidden either behind the search or from view due to login/signup.
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.
Screaming Frog handles this really well. Just do a scan of your site and sort the columns by Status Code. Find the page in question and there is a tab at the bottom for "In Links" that will tell you which pages it is linked from.
As I said you can setup a new view with an include Filter to only include your blog directory and view the demographic data through that.
Another method you might try is under Admin > Content Grouping, This will allow you to group blog posts together and when setting up the report, you will be able to select the Content Group under Filters.
If this is something you will need on an ongoing basis, it might be best to create a new view in Analytics with filters to just show the blog data.
Use the subfolder. The problem with subdomains is that they can be treated as a separate website and if that happens then the strength/signals do not pass to the rest of the website.
Same as others, the traffic from Semrush is usually a lot lower than the actual traffic. They probably use exact match search terms so a lot of traffic from mis-spellings, related long tail terms, variations, etc is missing from their data.
There is a lot that goes into ranking a site and generally the more authoritative the site, the more it can get away with. A few backlinks like the one you posted wouldn't even hurt a normal site. On top of that, you don't know if these companies have these links disavowed in Webmaster Tools. If you have SEMrush, check their rankings over time and estimated site traffic for anything suspicious. You can also check Ahrefs for anything unnatural in their incoming links graph such as spikes. Even with this you're only looking at a portion of the data and missing many link types that most backlink checkers don't show such as NAP listings or social/web 2.0 links which rarely show up in OSE or Ahrefs.
Look into them but don't dwell on what a few are doing. If you want a better picture, look at some of the sites from other major cities as well and look at what everyone in your industry is doing to find ideas how to improve, without wasting energy complaining that someone is getting away with something.
Where are they linked FROM? Are they pulled in a menu or a sidebar or are they linked internally somewhere else? If they are not being used, you simply need to delete links to them and they will disappear.
The og:description is Open Graph and used for sharing, the other should be
While Moz has many great tools with lots of features and benefits, I am not aware of anything from them to check for external duplicate content. You may try http://www.copyscape.com/ or copy and pasting sections of text within quotes to search Google for duplicates, or this tool can help as well http://smallseotools.com/plagiarism-checker/
It sounds like you are looking for a link manipulation guide. Don't buy social media links on fiverr. You also should not worry about link velocity if the links are natural.
More information on the business would help, but in general go ahead and claim profiles on social media and web 2.0 sites as this will help establish your brand. If you have a physical address, make sure you get your Google+ business profile and submit to the major data aggregators and other NAP sites. Look at the backlink profiles of your competitors or do a bit of searching to find sites in your niche where you can acquire links. Submit a press release about the launch, maybe do a few interviews if the site is something people would be interested in.
You're more likely to get help if you are more specific. Post one of the sites and I'm sure someone will take a quick look and see if there are any on-page issues. You could also take a look at your Google Webmaster Tools and export the links that have come in to look for spam, or maybe check the sites with ahrefs.com and look at the type of links and anchor text being used. If the SEO was using some sort of automated directory submission software, you should not only see these links but probably a graph that looks suspicious like a lot of links within a month and not much after that.