Specificity
Specificity is a very simple concept where the larger the number is, the higher the ranking is. There are 4 possible digits to be included: inline, ID, class, and element. The more specific a selector is, the higher its digit placement is. For example, 1234 would be 1 inline, 2 IDs, 3 classes, and 4 elements. As for the order of link pseudo-classes being link, visited, hover, focus, and active, there is really only one reason, so not much time needs to be spent here. Lower stylings in a stylesheet take precedence, so you want to make sure that the pseudo-classes that are supposed to be overriding other states go lower in the sheet.
Contrast
To view the contrast ratio by itself, you can use the specific element selector in the top left of dev tools and hover over an element. If it's an element that cares about contrast, you will see the ratio. Also, you can then click on the element to bring you to the proper css in dev tools, and opening the color pallette and expanding the contrast dropdown will display lines for allowed sections of color. In the accessibility tab of Firefox dev tools, you can drill down to text leafs, and the contrast ratio will be at the top of the right column.
Why Contrast
The main reason to contrast text and backgrounds is to support visually impaired users. With bad contrast, they might be able to barely use your site, if at all. If you think about that from a more selfish standpoint, that means they will go somewhere else, making you lose out on some traffic. Even if someone isn't visually impaired, they may also seek out other sites. I know that when I'm on the web, I don't want to put in the effort to read something difficult to see.
Accessibility Rules
I don't know why, but I found two different answers: Web Accessibility Initiative and Accessibility Guidelines Working Group. My best assumption based off the information I've seen though is that the WAI plans and develops the designs behind the rules, while the AGWG implements the rules themselves. There's even a third group that gets mentioned: Accessibility Conformance Testing. I think this one tests the rules and observes the implementations.
Summary
Overall, accessibility is important. We want to try to treat all humans equally, and you can even get in legal trouble if you don't. As for specificity, being careful how you implement it can help future people working on your site.