Polite forms are used to show your respect to listeners/readers, as you wrote. On the other hand, respect is towards the subject in honorific forms, and towards the target/object in hamble forms. As for humble forms, the subject must be the speaker or the speaker's in-group members.
When you are talking with close friends or your family members, you don't need to use polite forms. Even in this case, if the subject or target/object is, for instance, your teacher, you need to use honorific forms or humble forms, respectively.
e.g.
(saying to your friend) 先生が昨日おっしゃってたよ。(The teacher is the subject.)
(saying to your friend) 先生に昨日お話ししておいたよ。(The teacher is the target.)
In the same logic, if there is no target, the humble form お願いする is not used.
e.g.
明日雨が降らないように願った。
There is no target, the one you asked not to make rain in this sentence, so お願いした is not used here. (お願いした implies you asked god or heaven.) And when you say this words to your teacher, the polite form 明日雨が降らないように願いました is used.
Similarly, when the target of 断る is your friend, the humble form お断りする is not used.
e.g.
(saying to your teacher) たけし君の誘いを断りました。
(saying to your friend) たけし君の誘いを断った。
Hope this makes sense.