Is it encouraged to post unasked questions we know answers to if they seem useful?
Or is this only intended to be used when a question goes long enough that the postee eventually learned the answer?
There is nothing that says you can't answer your own questions if you know the answer. The faq explicitly says you can:
So one might say that's encouraged, especially where it adds value. And after all, that does benefit other people
Having answered Q1 the answer to this is no. I'd say it's explicitly intended to encourage people to contribute stuff they think needs answering. However, it does have the side effect of rewarding people who answer their own question.
If you post a question on SO you might still find the answer yourself later on. "Self-Learner" encourages you to post this answer on SO, instead of just moving on and leaving the SO question unanswered.
Other people that come to SO later and have the same question will benefit from this answer.