According to Buddhism and the suttas, do the Brahmas and Devas have any direct interaction with human beings? Please provide examples.
Are these interactions all positive or also negative?
Which ones are initiated by humans and which ones are initiated by Brahmas and Devas?
Could this explain some interactions between God and human prophets in other religions?
The God of the Old Testament sounds very much like the Mahabrahma of the Brahmajala Sutta:
Then a certain being, due to the exhaustion of his life-span or the exhaustion of his merit, passes away from the Ābhassara plane and re-arises in the empty palace of Brahmā. There he dwells, mind made, feeding on rapture, self-luminous, moving through the air, abiding in glory. And he continues thus for a long, long period of time.
"Then, as a result of dwelling there all alone for so long a time, there arises in him dissatisfaction and agitation, (and he yearns): 'Oh, that other beings might come to this place!' Just at that moment, due to the exhaustion of their life-span or the exhaustion of their merit, certain other beings pass away from the Ābhassara plane and re-arise in the palace of Brahmā, in companionship with him. There they dwell, mind-made, feeding on rapture, self-luminous, moving through the air, abiding in glory. And they continue thus for a long, long period of time.
Thereupon the being who re-arose there first thinks to himself: 'I am Brahmā, the Great Brahmā, the Vanquisher, the Unvanquished, the Universal Seer, the Wielder of Power, the Lord, the Maker and Creator, the Supreme Being, the Ordainer, the Almighty, the Father of all that are and are to be. And these beings have been created by me. What is the reason? Because first I made the wish: "Oh, that other beings might come to this place!" And after I made this resolution, now these beings have come.'