Noodp= No Open Directory Project
Noydir= No Yahoo Directory

These are used if your website is listed in one of these directories with information you do not want used in the results pages. This might be the case if you have old, outdated listings that no longer apply. They tell robots not to use information from these sources, and they are optional.

A good idea is to keep track of a couple of your competitors' domain rankings, so you can see how you are doing relative to them.

Another quote from the link that keszi provided:
"It's best to use Page Authority (PA) and Domain Authority (DA) as comparative metrics when doing research in the search results and determining which sites/pages may have more powerful/important link profiles than others."

So if you see that your site went down and your competitors' went down as well, you'll know not to be too concerned.

Here is a nice article on the subject: http://www.searchenginejournal.com/google-recommends-using-xml-sitemaps-rssatom-feeds-optimal-crawling/118364/

"Google explains the differences between the formats by saying that XML sitemaps describe a whole set of URLs within a site, while RSS/Atom feeds only describe the most recent changes. As a result of XML sitemaps containing more information, they are typically larger than RSS/Atom feeds. XML sitemaps are also downloaded less frequently.

As a website owner, which format should you use if you want your website to be crawled to the best of Google’s ability. Google recommends using both, explaining how the formats compliment each other."

Looking at the first one with Screaming Frog, there are 112 pages without descriptions.

Visually checking an example of those, http://sundancevacationsnews.com/, I see in the description, an empty description.

Checking one with a description: https://sundancevacationsblog.com/sundance-vacations-travel-advice/international/, I see

It just looks like some of them didn’t have descriptions added. Check back in Yoast again and look at the pages that Moz says have no description. Does anything look different in those than in the ones that do have descriptions?

I don't think the problem is the plug-in since both the pages with and without the descriptions are using it, and yes, Google will see the same thing.

If you have Yoast (SEO Plugin) you can do that in the settings. (Choose Titles & Metas, then click on the Taxonomies tab.) You can also do it directly, under posts > categories.

I did just this type of thing a little over a year ago and organic traffic is up over 300% now. We made the change mainly to improve the structure of the website(s), with more logical organization and better internal linking. We did do the move all at once (thousands of pages) but it took a lot of behind-the scenes planning to be ready for that.

First came the decisions about what sections and categories made sense for our site. (Using the URL structure to guide users around the site makes it easier for them to find what they are looking for and interlinking between related posts as appropriate is also good—and this helps a lot with search engines.)

Then came the organization of posts into their new categories. To make things easier, we kept the individual path names the same (so www.siteA.com/old-category/old-post-string became www.siteC.com/new category/old-post-string) and uploaded them into their new categories when the time came.

We also used this time to do a limited content review (posts with the most traffic) and we updated a lot of these. We made the choice to keep most of our old posts, even though in our market they can get outdated quickly, to conserve any links we may have acquired. (The main site that we were directing to the new site was pretty old and had picked up a lot of links over time.)

We could have done a more complete content review before the changeover, but in part we wanted to see how these posts did under the new structure—we did get renewed life out of some of them, and we further updated and optimized those.

In conjunction with the export of the old sites to the new one, we made sure to 301 redirect all of the old posts to their counterparts on the new site. For the posts we chose not to bring over, we 301 redirected them to a related post in the same category.

We still occasionally come across things that need to be fixed—old posts that need redirecting/updating or 404 errors that need to be tracked down (one big issue we found was a lot of old pages had old links with hard paths to the old website root domains, causing a bunch of nasty internal not found errors—not good!) but overall we are happy with the change. (Up 308%!)

In your chrome browser, there is a little "hamburger menu" on the top right (three horizontal lines, stacked).

Click that, go to tools > extensions and you should be able to delete it there.

ps- What do you find that it covers up?

Way back in 2012 Matt Cutts said:

“I read a post by someone offering new top-level domain (TLDs). They made this claim: ‘Will a new TLD web address automatically be favoured by Google over a .com equivalent? Quite simply, yes it will.’

“Sorry, but that's just not true, and as an engineer in the search quality team at Google, I feel the need to debunk this misconception. Google has a lot of experience in returning relevant web pages, regardless of the top-level domain (TLD). Google will attempt to rank new TLDs appropriately, but I don't expect a new TLD to get any kind of initial preference over .com, and I wouldn't bet on that happening in the long-term either. If you want to register an entirely new TLD for other reasons, that's your choice, but you shouldn't register a TLD in the mistaken belief that you'll get some sort of boost in search engine rankings.”

and I have not seen anything to indicate that this is no longer true.

Some people like to get the new tlds because they feel that they will be attractive to the user, that if for instance people see a .tv they would choose it over another page because they would think that a .tv provides a better video experience.

This may be true, but on the other hand, there are plenty of people who no longer think of tv when they think of the video experience...

Yes, for the most part "index, follow" is what you want on your pages.

But no, the "noodp, noydir" tags do not prevent you from being in the directories (though as Alan pointed out, the Yahoo one isn't around anymore), they just prevent the descriptions from being used.

Google does not always use the title and description found on your page, it sometimes chooses something it deems more relevant. Sometimes this is the description from the Open Directory Project (DMOZ). Sometimes this is not a good thing to choose.

Maybe your site was quite different when it was submitted to the directory, and the information there no longer applies. You want to tell Google not to use what is in there, so you use noodp in the header.

Whether you use or do not use "noodp, noydir", it won't hurt your rankings.

The only reason you might want to make sure to use them is if you saw unexpected content in the descriptions of your pages in the search results pages, and you had reason to believe the descriptions came from DMOZ. In that case, to prevent that from happening, you would use those additional tags, along with "index, follow".

Right now, the MozBar only works in Chrome. (Scroll to the bottom of the thread to see the latest update.)

I love this add-on (I especially love it when I do a search and see all the data on each result) but you can get the same information by using the tools inside Moz, you just won't see it immediately as you look at different pages.

I myself prefer Firefox and was disappointed when the MozBar stopped working there. So my compromise is that I still mostly use Firefox but just switch to Chrome if I am doing something where the quick information from the MozBar would be useful. You could do the same with Safari.

Alt tags are used to convey information to people who cannot see the images, so they should always be used (unless the image is just decorative). If the images are different, use different alt tags.

Google has a number of ways to find pages, including links from indexed pages (whether internal to the site or external) as well as sitemaps and Fetch as Google.

Most of the time when you come across a page like that (one that has few if any internal links) it's not an organic-traffic oriented page, it is set up for some other purpose, like a landing page for a marketing effort.

As a general rule, a link that anyone can get by just placing one there is unlikely to give SEO benefit. And as mcncll said, most of those types of links are nofollow, anyway.

The benefit of the type of the type of link you are talking about is exposure and possible referral traffic. (Assuming the answer that is posted is a good one, of course.)