I really enjoy reading through the related posts. However, some of them can be quite old. Is it proper etiquette to upvote those that I give those that I find deserving? Should I consider a question that has not had any recent activity to be settled, therefore the upvoting has no purpose?
You should absolutely upvote! The fact that it's old doesn't make it not worthy. In fact you should even suggest edits to old posts to improve them. The only thing we would advise against is editing dozens of old questions in one go, as that can flood the front page (but upvoting won't do that).
Yes, please do. Voting serves two purposes: indicating the community's collective wisdom and confidence by bubbling the best answers to the top, and giving reputation to the users who write the answers we thereby give our confidence to.
Adding your voice to our confidence in an answer or question is still useful after the original asker has marked an answer as accepted, since people find these questions long, long after they're asked, either by browsing them like you do or through search engines. To a new reader looking to solve the same problem, the answers' age doesn't matter to whether they help them.
In fact, questions that aren't useful to more people than the asker get closed as "too localized" – we strive for questions that are at least somewhat widely meaningful to answer, so that they're remain a useful resource long after the original asker has solved their problem.
Giving reputation to users (which upvoting does) who wrote good answers quite a while ago is still useful because reputation is how users gain more privileges and ability to shape the content that is hosted here: editing privileges, close-voting for things that don't belong, and that kind of thing helps maintain the quality of the site. By upvoting old, good answers, you help by saying you think these people know what they're talking about. Increasing the privileges of users who have a proven track record of writing answers that "fit" helps keep the site in good shape.