Some posts don't have a link on the right (named
active) that would take me to the latest edited post on a thread. What are the criteria?
active tells you when a question was 'last active', and links to what activity there was most recently.
One of the answers for that question, or the question itself was edited, or a new answer was added; the link leads to the post that was last updated or added. It is only shown if there is at least one answer; it is not shown on questions without an answer.
In the first example, at the time of this answer, the active link points to a new answer added 2 months ago; no other new answers or edits were made since then. The second example you give has had no answer, so no link is shown.