Who decides when the status of a "feature-request" question should be assigned?
Moderators or employees. Usually that is only done by employees, though. Sometimes when there is preexisting consensus or previous questions about the same feature-request, moderators may tag a question with the appropriate tag, and then close as duplicate.
In general the [status-*] tags are reserved for employees, though. This means, Devs and CMs assign these, when company-internal discussion has come to a consensus. In edge-cases they also refer to previously established community-consensus, but that's seldom.
Are there any rules about how soon the status should be assigned?
No. This happens when the people in charge get around to it. But when a status is assigned, that status is usually final, and as such status assignment happens after quite some time.
Should I give my own input on a "status-declined" question, even
though it is now declined?
Sure you may do so, but from my experience there's seldom necessity to do such, unless the situation changed significantly.
If I think more could be added to such a question, or that situations
have changed enough, should I ask a new feature-request or add to the
If you want to add to the old question, you should do that. But for significant change of situation, it is advisable to create a new question, linking back to the previous question and explaining the differences.