Meta Keywords are important? Only those that show content on the page are important. The metadata description would be an example of an important metadata, the metadata keywords (keywords) would be an example of metadata that is not important or not relevant. The keywords must be in the content of the page.
Do not add nofollow to your internal links: With this you are diluting your pagerank, you will find a whole post dedicated to this topic in my blog. Here is a point of debate. What about links to registration forms, login, forgotten passwords, etc? Matts Cutts continues to say that using nofollows can do more harm than good, on the other hand there are many voices that indicate that it is good to add nofollow to this type of links. While there is an alternative way to properly configure robots.txt to avoid indexing areas that would produce duplicate or poor quality content. I do not add to these types of links.
It is the first link of a page more relevant than the rest. No. Google crawls all the links, what really matters is that it is not broken but not the order.
Import the age of the domain, how do you get the age of the domain? . No, it does not matter if the domain is 4, 6 months or 10 years old. Google does not get the age of the domain by looking at the whois since it is not always available. Google determines age by comparing the first time you indexed a page from that domain or posted a link to that domain. (Matt Cutts from his channel Googlewebmasterhelp).
Do the links import from sites like Twitter or Facebook? Yes, they matter the same as any web. A profile on a social network also has pagerank, my pagerank on twitter is 3 at the moment. Now something happens with social networks. Facebook for example has privacy settings and therefore a profile may not be public and Google will not index it. The more public content in that profile, the more interesting for Google and more Pagerank and therefore the more important links that leave that profile.