"it would seem strange from a UI point of view not to have a consistent navigation."

You hit the nail on the head, imagine is a website like Amazon removed the link on their logo to the homepage from the homepage, some people click this on the homepage just because they're confused and if they don't see a page refresh they may be upset. It's also a LOT more work to implement this.

I would argue a consistent navigation is good, as Google likes to follow a good structure, it's just causing you potential problems, what if you're using a CMS and you're on the blog, then you go to a blog article, do you remove the blog menu link as you're within the blog? There's just no real reason I can personally see for it.

They used to be used quite heavily. Nowadays majority of the major search engines don't use them at all. The only one I believe still does is Yandex, of which it's a minor signal then.

Just to expand on this, I found the following quote from a Moz member of staff:

"I wish I could give you IP addresses, but they change all the time since we host Roger in the cloud. There's not even a reliable range of IPs to give you. You can totally whitelist the useragent rogerbot, but that's the only reliable information about the crawler you can go off of. I hope that helps but let me know if there's any other solution you can think of. Thank you! "

From a previous question: https://moz.com/community/q/is-there-a-whitelist-of-the-rogerbot-ip-addresses

I would use the search console "fetch as google" it can take a few weeks for Google to crawl and update your site in the serps. Usually I leave 4-6 weeks for any change (on a small site) with larger sites normally being crawled more frequently. When you do cache:yourdomain.com in google chrome, is the time listed sooner than you did the changes?

An answer from one of the founders (no longer in the company) who I have on skype, I stripped out a couple of things from the chat (my posts and a couple of irrelevant bits):

[16:08:31] A Founder: that's a difficult question to answer really
[16:08:43] A Founder: is it worth £80 a year ?
[16:08:51] A Founder: I would doubt it to be honest
[16:10:07] A Founder: apparently I cant reply anyway
[16:10:37] A Founder: I aint a pro
[16:11:09] Me: If you want to write it out I can reply for you
[16:12:48] A Founder: well if you want to tell him scoot also offer a free listing and I am happy to talk to him but cant as I aint a pro
[16:13:08] A Founder: and yes I was one of the 3 founders
[16:13:27] A Founder: ya they now bulk list you
[16:13:46] A Founder: 500+ directories, that to me sounds so spammy
[16:14:13] A Founder: I would claim the free listing and say thanks but no thanks to the rest
[16:17:36] A Founder: but feel free to post my thoughts if you want

It'll vary because of the crawlers, each company will have a different amount of sites in their database, and they will also have a different process to get their data live in their console. Honestly I would take each with a grain of salt and just try and use them as a rough guide.

I have had something similar, this is response I received:

You don’t have canonical tags on the URL and that’s expected.

On pages where BVSEO is implemented, canonical tags must be updated or removed when the product contains more than one page (more than eight) of reviews. BVSEO paginates the product page so all reviews are in the search engines’ index. Canonical tags that point away from a pagination URL will cause search engines to ignore the paginated content.

When any of the BVSEO pagination parameters are present (bvstate, bvrrp, bvqap, bvsyp, bvpage), do one of the following:

•Remove the canonical tag. This is the most common, recommended solution.

•Append the "name=value" pair to the canonical URL.

Something i'd never thought about: http://www.searchenginepeople.com/blog/anchor-links.html

So looks to not have an impact according to that article.

Yes that looks correct, I would add an x-default for the rest of the world. this is a good article: https://hreflang.org/use-hreflang-canonical-together/

http://www.myseosolution.de/downloads/mobile-hreflang-canonical-fixed.png Is a great image to explain things.

Yeah I believe that regaining the DA back shouldn't be an issue for the old domain. It won't be instant, but shouldn't be a massive amount of time before you get back to where you were previously.