I suppose we could say that the disciples respond naïvely to the calming of the storm, but “rebuked” also conveys authority, doesn’t it? How much of this is Matthew’s dramatic method?
Your reflections on prayer in John’s Gospel are apposite. John 11:41 seems to imply that Jesus has already prayed (“I thank you that you heard me…”). He then commands Lazarus to come out. We don’t know at what moment Lazarus was resuscitated.
The rain is held back by Elijah’s word, but the drought ends when God sends him to Ahaz, saying, “I will send rain upon the earth” (1 Kings 18:1; cf. 18:41-46). Elijah does not directly or personally cause the drought either to begin or to end. But presumably the point is that he has been in some sense authorised as a prophet to speak on behalf of the God (the word of the Lord comes to him) who does these things.