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Generally, I like to see them in place with any site we review, but here is a great WBF that outlines some examples of when to use canonicals.

The most common thing we see with Shopify is that the categories are often a mess due to lack of planning and understanding. They call them collections, and it's the equivalent to doing tag/category cleanup on a WordPress site to help clear out low-value content. Another common complaint is that the blog forces you into a bit of annoying URL structure (ie. /blog/news but works well if the content is solid.

Congrats on the new site. Moz has a great resource to plan for a site migration and should cover what you need to watch out for.

Make sure products are in your sitemap and it has been re-submitted. You can also submit your products to request indexing for them in Google Search Console.

If both are important to you, than have both. The intent on those two things are different and will be looked at as such for search.

Using the proper structured data as Roman mentioned for both types of content will help search learn about your content faster and provide opportunities for rich results in your market.

While you may not want context indexed, it's still valuable to be crawled and access your most important content like products.

If you are blocking your /collections pages, Google will not be able to see that page's meta robots set to noindex, causing an issue for you. You may consider allowing robots to crawl your /collections pages but noindex them if they are low value or duplicative.

You'd see more value out of a proper full SSL installation than troubleshooting or implementing a healthy setup for mixed URLs IMO.

Recently @JohnMu mentioned that site: is not reliable to check pages in index. The new GSC should help you better understand how Google is seeing and valuing your content.

Regardless can you change it so that root file without params is a page that has value? and potentially a page that provides a means of navigation to your parameterized results? This would be a more search friendly setup IMO.

\The redirects for the old .html structure should go to the preferred  domain, ie: https://nonwww.com/most-relevant-new-location

CNAME is not a redirect and just points the user to the right server and I don't think switching is going to have any impact on what you're seeing. Some services like Cloudflare prefer you CNAME your www and non-www to the server to help protect the server IP.

The switch to https is an important one and you want to be sure that you take every step to make that smooth transition, ultimately getting https pages ranked instead of your http versions, and then users will be hitting your preferred URL scheme.

Yes! I read the example backward. I'm with you! All pages should point to C.

I'd have them all pointing back to C so it's a little easier to manage long term. G just updated some of their docs related to canonical URL use cases with some great examples. From this page:

You can use a tag in the page header to indicate when a page is a duplicate of another page.

Suppose you want https://example.com/dresses/green-dresses to be the canonical URL, even though a variety of URLs can access this content. Indicate this URL as canonical with these steps:

1. Mark all duplicate pages with a rel="canonical" link element. Add a  element with the attribute rel="canonical" to the  section of duplicate pages, pointing to the canonical page, like this one:

2. If the canonical page has a mobile variant, add a rel="alternate" link to it, pointing to the mobile version of the page:

3. Add any hreflang or other redirects appropriate for the page.

They don't touch on the chain of canonical URLs you suggest but I'd have them all pointing to C since it's a scalable change.

[edit: updated to match example in OP]

I think you'll probably need to put some thought into this as outreach is all about quality. Your recipient is busy so be direct. Get to the point and make sure they understand the value your piece is offering. Make it relatable, helpful, authentic and timely. If you can show them what about your story is compelling and relatable it may win their buy-in.

I worked for an agency that did this manually and had about 1500 contacts they would choose to email based on the story or PR push. We used a simple email distribution app campaign monitor and A/B tested our emails for stronger response rates. It worked well at a small scale but had limitations to it.

Someone from Moz will probably give better insights but the DA metric may not be impacted by your change but rather the update to the tracking index from Moz. If you read into the DA metric they provide I believe it is relative to their index and will fluctuate based on data they hold - primarily about links and site quality as a whole.

I'd be surprised if pruning your content put you in a place where DA was negatively impacted as a direct result.

It's getting harder and you may see a gradual decline for that ranking if it does not match the intent. Some queries are harder than others and will have mixed results so it always will depend on what you are seeing longer term for trends and ranking performance in your space.

Go to Google Search Console and submit the page for indexing again to make sure you get quick attention.

Take a look at the top results manually for the query you target and you should be able to better understand the intent. Depending on your niche or vertical, pricing on queries in Adwords can also help as queries with a higher purchase intent (for example) will have higher CPCs.

It's a signal that may be valuable for sites but one that may not have a huge impact on it's own.

I like to have shorter URLs because it ends up being easier and more friendly to share. Longer URLs can be a deterrent. I also like to pay closer attention to the click depth of the page, not just length of the URL.

I'm not sure you'll be hurt by a long URL like:
http://www.yourtld.com/blog/02/08/18/some-crazy-long-slug-nested-with-dates-that-triggers-moz-errors

I would bet you can get that page ranked if the content is valuable enough, even with a longer URL. But the issues start to pop up If you have a site that has content only found by browsing the nested pages it is a larger issue.

For example:
http://yourtold.com/services/cleaning/windows/indoors
This is an example where I'm really worried about the length, but more importantly the overall structure of the URL and site. It may be difficult users, and crawlers to find this content making it less search friendly overall when the content is 4-5 layers deep.

For the second/duplicate page set the canonical to the page with original content. Is it just a vanity URL that you need  or is there something different on the page? a 301 may be a better choice to offer a vanity URL.

More here about your options with duplicate content: https://moz.com/learn/seo/duplicate-content

Take a look at the search results for some of your target queries. Take the top ranking site URLs and put them into Moz's keyword explorer and use the exact page option.

This will give you a sense of the types of keywords the content showing up for your query may be ranking for and help with your research.