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Can you go to Google Analytics and go to Behavior > Site Speed > Overview and see if there is any particular browser that is loading really slow and throwing off the data? It could be that the mobile version is not well optimized and this makes up a lot of your traffic, or that cell service is slow in the market, or there may be some browser specific issues.
http://tools.pingdom.com/fpt/#!/c7KWrp/www.nyc-officespace-leader.com
I just ran a test and got a load time of less than a second for your site. Now this may be without much server load, but it looks like you already use caching and I don't see anything too out of the ordinary. It may be that your server slows when it gets loaded down. Maybe look into caching pages into ram or an ssd on the server side, but I don't think there is much more on the website side you can do to help.
Go ahead and create the redirects but you also might want to submit a change of address in Google Webmaster Tools.
I'm not sure what would be causing this. It looks like the pages did exist on the services subdomain at one time. Maybe try adding the subdomain in Webmaster tools and removing all pages. You might also want to add a robots.txt to the subdomain and disallow bots from crawling.
As the parent company, I would want any individual work done to benefit the main site and as a store owner, I would want to have some benefit from the parent company as well. There need to be policies in place to prevent bad practices, but it should be all stores and the parent company helping each other. If they want to be treated as a separate entity then they should probably build a website themselves on a separate domain. Most major retailers have the stores in subfolders. Go check walmart.com as an example.
Best for SEO is with a subdirectory. Subdomains can be treated as separate websites.
First thought is a plugin from your antivirus maybe? Try with addons/plugins disabled.
A quick look and it doesn't seem like you have a lot of links yet, which isn't surprising since you haven't launched. You will have some work to establish your brand in Google. It might help to grab a business Google+ page, as it looks like right now you have a personal one. Also, in the link to your G+ profile, never use the /b in the url, this is part of the admin page url. Getting ranked for the term zing means you have to show Google that if people search zing, they are looking for you. I think this will be a difficult task with the word, but as was mentioned start with social profiles before launch, after launch focus on NAP listings, a press release for sure, and niche specific links. If I named a company Michael Jordan, even if I did everything right to establish a brand, it's not likely I would rank when people searched Michael Jordan, so just keep that in mind. There are many other sites using zing in there name or even having the domain zing.com. You have an uphill battle my friend, good luck!
Great answer Oleg, I would just like to add that on top of the social presence that you should also be looking at NAP listings for the company.
They should have started with the fact that you have 3 versions of your site:
To address your questions, yes there are some issues with how content is displayed at different screen sizes, and while this may affect UI slightly (an example would be your NAP listing in the footer where company name is centered and the address / phone are left aligned) these issues won't really affect your SEO.
For your second question, this again has no effect on SEO.
For the third one, I doubt your target keyword is your company name. Bolding is a very small SEO factor, but it seems like you would want to target voter lists and not your brand name.
Short answer: yes. When you append the location to the title tag (along with other key areas to make the page more focused in an area,) then you are telling the search engines that your target is in that city. When searching without the city name, as long as they are in the area, they will likely see wikipedia, some news, and some other big sites but you will also see some local results mixed in, sites specific to that area. If set your location to another city in another state and search, you will not see the same ones that are local to your market, but ones that are specific to the city you're searching from.
If everything is done properly as in redirects ready to go, as good or better on page optimization and internal links in place then you should see no drop at all. If things are done better on the new site you can potentially launch with higher traffic.
Are you trying to check a lot at once? if not, just use the site: operator, i.e. site:abc.com/page
Fix the alt and title tags on the images, and while you're at it rename the images so they are relevant as that was likely not done. As far as meta descriptions, that will not help you rank, but can affect clicktrhough rates in the SERPs. My thoughts are you probably have a lot more cleanup to do and adjusting meta descriptions should be a lower priority task.
In addition to Monica's response, under search tools you can set your location. So set your client's city and see what they would see without any bias towards account or history preferences.
Ahrefs, Majestic Fresh Index, and Google WMT will all tag links with the day they were discovered.
You might try pinging the site out or just building a link to the site.
In Google: site:competitorsite.com yoursite.com
In screaming frog: set custom as your yoursite.com and crawl the competitor's site, then under the custom tab should be any links that refer to your site.
Options +FollowSymLinks
RewriteEngine on
RewriteBase /example1/
RewriteRule ^example2/(.+)$ /$1 [L,R=301,NC]
Try this.