Google has recently changes the way sub folders work so Google now treats sub domains as the same website,

That been said the sub folder is normally a far better option due to internal linking factors behind the domain and it works as a more powerful option over time from my experience.

You can do internal re directs, we have done 100s over the years and not had many dramas, just make sure you map out the correct re directs to correct folders.

I would really research the level of localized traffic per sub folder, research into the new Google changes into sub folders, and look at Google ad preview for GEO based serps based on your domains based per state to see what the potential problems could be.  You really need to do a risk analysis for the client, we have done a few of these recently for global travel clients who have had similar issues.

I would not give the experts a blog on the wordpress sub domain be sure that when they blog it is on a sub folder for your website so when links are built they benefit your site directly and not wordpress.

I have seen some results for Wikipedia where you pull your hair out hehe, but the thing is the site is soo high authority and the internal link value it holds.

To be honest I have had experience taking down Wikipedia where you deal with big brand websites and you can highly target the site.

Really do some analysis on the links the wikipedia page has, see what you may be missing if content is not the problem.

Just keep pushing fresh content and social signals too if you can try and implement people to search for your website and drive higher CTR on the serp page.

Blogs are great for SEO because you have a platform for search engines to provide fresh new content, the problem with static websites is that the content is always the same. This is where blogs always push new content.

Well the best bet is to have your blog located on www.website.com/blog  people make a mistake when they have the blog on a sub domain because you don't have the right flow of link juice.

Exact match domains can be good, but I do agree they are becoming less powerful compared too say 2 years ago.

You can still get the following with a EDM:

• Good for branding

• Great for type in traffic selling Auto Insurance, 2-3% of people direct type in domains example autoinsurance.com

• EDM SEO ability still evident yet it is dropping.

Another method I have been using for a while, just to check the number of indexed images:

1. Search for site:www.website.com

2. Scroll to the bottom of the page, and hit "switch to basic version"

3. It will then show the total number of indexed images via Google.

I am sure their are other ways you can do it via crawlers and analytic's reports too.

To add too the comments above specific spammy backlinks can infact hurt your site,

For example if all of a sudden you see a number of links to your website with anchor text to adult terms pointing to your website with your url from adult based websites. I have seen targeted spam in this way affecting websites.

But from what you explain the links that have been built by the prior designer do not seem tat bad at all, I would not worry too much.

Also check how much traffic the tags are currently getting, one site I have looked at in the past had like 16k uv a month from some tags on the site so proceed with caution also I agree with the advice above as well.