If you’ve seen anything here about God’s omnitemporality, you may recall that any tensed verbs we use (the only kind we have) have to have qualifiers attached. So ‘regretted’ is past tense and does not strictly apply. Maybe what should be more potent is the regret we cause him who is the eternal Now. And I routinely fail to be as sensitive to that as I should be.
Others may differ as to what the image of God in us means, but personhood I think is an attribute that is implicit – that includes feelings. So God can feel pain (and we’re told that in Ephesians 4:30).
Others can speak to the literary types and their associations with the cultures of the time where I certainly cannot, and to the historicity of the text, and it is certainly more than unlikely it was the first rainbow ever. But God may just have given Noah such a providential gift as assurance of his continued faithfulness to mankind.
I remember when I was at a low point several decades ago (about four ; - ), the timing and placing of a rainbow where I happened to be able to see a small arc of it against blue sky was astonishing. It is difficult to describe, but it was early morning through a small window partly covered on the inside and partly blocked on the outside by a wall perpendicular to the one the small window was in. There was also a large and fairly bushy pine obscuring even more of the sky. So the view of the sky was particularly limited. My confirmation bias1 let me be comforted and encouraged by it, inferring it to be a providential gift from my faithful and sovereign Father. 
1 As noted just yesterday,