+1 to what Ross said. Subdomain hosted elsewhere won't have any impact. However, you should consider moving your subdomain to the sub-folder if that makes sense for your SEO Strategy.

Have you also seen any impact in traffic during the same timeframe?

Take a look at this post on Moz - https://moz.com/blog/seo-changes-using-google-tag-manager. Also, take a look at https://productforums.google.com/forum/#!topic/tag-manager/Ilxks3tQKrg. Personally, I wouldn't recommend doing this via GTM. Noindex and Schema specially. They are both important for SEO and are better off done via the CMS.

If your AMP is setup correctly, I wouldn't worry about this. Do you have the correct amphtml tag and the reference back to your canonical?

Eric, Have a few questions for you:

1. Do you have executive buy-in to do SEO Work?
2. How much SEO potential is out there for your website to rank?
3. How well does it rank today?
4. How big are your Top 3 competitors? Have they been growing last 1-5 years?

If you can demonstrate the size of the opportunity you have and prove it's achievable with a smaller project, test or experiment, you might have "unlimited resources" ;). Just saying :).

I highly recommend Screaming Frog on top of Moz. It can do a lot of Ad-Hoc crawls and help you diagnose potential issues. Try and play with the free version. Depending upon the site of the site, you might be okay with the less than 500 pages. However, at $200 a license, it's not much for a larger site. Imagine what a bug could cost you? 

Directory links are the "manipulated" links of yesterday. I would strongly suggest to ignore them. Great details Alick300. I would suggest to spend some time reading Moz's Link Building and SEO Guides i.e. http://moz.com/beginners-guide-to-link-building

It's very easy to get in trouble with the wrong links.

Was this a Wordpress blog and did you install a plugin to do these changes ?

Yes, it will. Also looks like custom code, it depends on how the header is coded. But it should work. Test it, if you can. This should solve your problems relatively easily. If nothing works, you can always do a robots.txt deny for /property-search-page/?* pages, but that's not a recommended solution. Try the canonical way to see if it works first.

I checked the homepage and the housing page and both have the blank description tag. It definitely looks like a plugin/theme issue. Looks like your All in One SEO plugin descriptions are showing alright. Check in your theme files, specially header.php and see if there's an empty description tag in there. You never know, it happens sometimes

Taylor, you are 100% on the right track. All the answers exist in your question.

#1. These are "redirect notices", not errors. More like warnings.
#2. As long as they are canonicalized correctly, which you said "do I need to do anything if both those pages are canonical to the parent product".

There's absolutely nothing you need to do. You are good. It's always good and important to verify these technical SEO issues. I hope this helps.

I worked on a B2B with a similar problem sometime back. The business decided to implement a Request for Quote system. And there was no impact on the rankings.

I am presuming all those domains are linking to each other, correct ?

Are they regular or nofollow links ? It boils down how much authority you have on your main domain as well as the other domains. If I were you, I will keep the main e-commerce website on one server and everything else including niche blogs etc on a different server. It's not just SEO, but also security issues.

Essentially, to answer your question, it may not be hurting you to have the niche blogs, a forum with user generated content, the articles site and the corporate site on the same IP/server, but it would help you a lot more if they were on a different server, possibly different Class C IPs. So, you will gain from these links being on a different server. Keep in mind, these links are important for you and its good to increase their value by hosting them separately, because these sites are links that your competition can never get linked from. I would also consider doing a nofollow on them, and that's just my thoughts. I prefer lower risk. Again, it depends on what your e-commerce website's link profile is.

I am sure they did, but we were never able to have a read on it because price data was never added to the site. We just started measuring the Call to Action / Conversion as a successful RFQ or a visit to the contact page from these product level pages.

Eric, Have a few questions for you:

1. Do you have executive buy-in to do SEO Work?
2. How much SEO potential is out there for your website to rank?
3. How well does it rank today?
4. How big are your Top 3 competitors? Have they been growing last 1-5 years?

If you can demonstrate the size of the opportunity you have and prove it's achievable with a smaller project, test or experiment, you might have "unlimited resources" ;). Just saying :).

I agree with what you are thinking. The biggest effect would be if you can move them all onto one domain name (sub-folders) and setup 301 redirects. Keep hosting those domains forever since the 301s would stay only as long as you own the domains and continue to host them to serve the 301.

Moving them to sub-domains might be minimal / zero effect. I only see risk in doing that.

Ask yourself: Does it help the users in integrating all the content into one big website ?

Directory links are the "manipulated" links of yesterday. I would strongly suggest to ignore them. Great details Alick300. I would suggest to spend some time reading Moz's Link Building and SEO Guides i.e. http://moz.com/beginners-guide-to-link-building

It's very easy to get in trouble with the wrong links.

I agree with Ian 100%. It does not make sense (Even though that pingback link is nofollowed). Does it help your user ? Would it be useful to have that link available to them ?  Think about the user experience and in most cases, we get the correct answer, which is almost certain to be white hat way of handling the situation :).

Great answer Ian.

I just responded to this exact question. Here's my answer and a link to that question:

Honestly, my advice would be to grab a list of your backlinks using both Google Webmaster Console as well as the OpenSiteExplorer and merge them into a spreadsheet and get rid of all the duplicates.

Next step would be to identify which of those links are spammy and you'd be better of having them removed. This is in my opinion the hardest part depending upon the volume of sites/links.

Then hire somebody to find email addresses of the websites where you want links removed. Finding something on the page and if nothing else, using whois. I would then send an email to each one of those contacts and in a quick short email, tell me the URL where the link is located and your site URL. Tell them to remove the link right away since you have received a Google Warning. I would imagine this taking care of a good portion of those links. I would send another email in a week and then again for a total of 2-4 times to see if you get a response and get the link removed. When nothing else worked, offer then $10 for the link removal and that should gain their attention. If that does not work either, I would suggest you move on.

I hope this helps. You could get somebody on odesk.com or a similar site to get all the labor intensive work done.

Enam, I would not worriota out it. This is a natural link. Think of other social networks like twitter. If you were to tweet your link and 10,000 users retweet it, you have that many links from different pages within twitter.com

this s the nature and structure of the website, don't stress yourself about this. If this was coming from a crappy domain or spammy bloon other it would be something to worry about.

I hope this helps. Have a good weekend.