Regarding Jonah 3, granted, some wish to view the account anthropomorphically (e.g., Calvin); I have reservations about such an approach for the following reasons:
The Hebrew word used to describe God's "change of mind" is NaHaM. Concerning this lingual symbol, G. J. Wenham writes:
"'Regret' or 'repent' may suggest a change of attitude, but when God 'repents,' he starts to act differently. Here [Gen. 6:6] and in 1 Sam 15:11 and Jer 18:10 he regrets some good thing he has done for his people, whereas in Exod 32:12, 14; 2 Sam. 24:16; Amos 7:3, 6 he repents of some evil he is carrying out. That God should change his mind might lead to his being accused of capriciousness, which Scripture firmly denies: 'God is not a son of man that he should repent' (Num 23:19; Cf. 1 Sam 15:29). Such remarks obviously raise various questions for the doctrine of divine sovereignty and its correlate human responsibility, but theological systematization is hardly the concern of the biblical narrators. For them divine repentance is a response to man's changes of heart, whether for better or worse" (Wenham, J. G. Genesis 1-15. Waco, Texas: Word, 1987, 144).
I concur with Wenham that the "biblical narrators" or writers depict God responding to human changes, "for better or worse." That is, when God "changes" in Scripture, He is simply responding to the actions of his creatures. To illustrate, before I began to exercise faith in Christ as Savior and King, I was apparently one of God's enemies (Rom. 5:8ff)--the wrath of God remained upon me (John 3:36). But after taking the necessary steps to become reconciled to God, God's attitude toward me changed from one of wrath to a demeanor filled with love and kindness (Titus 3:3-7).
When God made this change, however, it was not an alteration of His essence: the change was relational and responsive to changes I had previously made. I would even contend that it was an actual rather than just a perceptual change. In sum, I believe that change in God is real. So while Jehovah is immutable as the ever faithful Rock of Deuteronomy 32:4; James 1:17, He is able to change relationally, responsively and possibly with respect to His emotional states. The pre-Nicenes held interesting views of divine emotions that were later superseded by the medievals. Yet the Hebrew prophets speak of God rejoicing or feeling pain of heart.