The age of a domain has a value, and figure the age of a link does too. How would you estimate the age of a link, and would you limit the age to the age of the domain?
It's hard to determine the age of specific links retroactively because you would have to know when the search engines found the links, however, in some cases if the links are within articles you can look at the date the article was published, many sites especially news sites include the date.
Also you should be able to get approximate dates going forward using something like majestic SEO if you bought a link report each month and stored them in a database you could keep track when they first appeared in the report.
Majestic SEO also has a back link history report, which shows aggregate numbers of links they've discovered pointing to a certain domain over time, this usually sufficient to get a historical view of competitors linking habits and much more efficient for most webmasters.
The age of a domain plays in a little bit when considering SEO. This rule is setup to avoid people creating multiple sites for SEO purpose and thus using them to promote a single site.
I have never heard of any SEO importance being given to the age of link. Doesnt mean that it isnt so.
My primary concern is this. Good SEO principles start with the design of your site, how your content is structured, written and how your site is coded.
Next focus on exposure, making sure that your content is properly aggregated and focus on building backlinks of real value.
After that, get back to business. There is a point where you are focusing on SEO far too much and taking energy away from your product or customer service.
Something of a trick question.
The age of the link dates to the time the link was made a part of the content associated with the domain - given that it is effectively possible move content's association between domains, it would be difficult to determine how old the link is if you are not actively monitoring the internet for the content in which the link occurs in the same way a search engine would.
To the second part of your question, the age of the domain is not a delimiter for the link's age (for Google, at least) because the link may have originally existed in content at domain0.com before domain0.com's content was permanently redirected to domain1.com - the metadata used to calculate the value of the link transcends domains and, theoretically, the value of the link would as well.