"In what way is Judah confused about its identity, according to verses 2-4?"
They have forgotten they are children of God, or perhaps they are aware that they are children of God, but are in open rebellion to Him.
Verse 3 referring to the ox and the donkey seem to imply that Judah has forgotten that they have an owner and a master, or don't understand what that really means (in other words, how they should relate to God the Father). Verse 4 implies more of an open rebellion, referring to forsaking and despising.
"What are the consequences when Christians today suffer from such identity confusion?"
I think we often forget that we are children of God. Perhaps this is colored more by my experience, not growing up in a home where God was discussed & where we only went to church at Christmas & Easter (if even then), but I think we tend to think we're on our own down here, and we celebrate our individuality & all that we humans have accomplished (for instance, the triumphs of science & the scientific method). But when we run up against our limitations, and all of our flaws, and the evil that exists in the world, we forget about God, and we forget to trust God. This leads to anxiety, despair and hopelessness. We need to remember that God is good, He is all powerful, and we are His.
"What injustices does God accuse his people of in verses 15-17?"
He accuses his people of forgetting about the needs of the disadvantaged -- the fatherless, the widows. Again, this may be influenced by my experiences, but it seems to me that God’s children had been leading selfish lives, looking only to themselves, and not to others.
“In verses 18-20 God argues that their behavior is ‘unreasonable.’ Why is it unreasonable? What does God offer as an alternative?”
It’s unreasonable because God’s children have forgotten their place in the grand scheme of things -- they are (and we are) His children, His creation -- in other words, we are His. God offers to be reasonable about this -- if we accept our place & if we’re willing and obedient, he’ll provide for us -- we’ll eat the best of the land. Only God can make a promise like that, & deliver on it. And I think, like any good father, he outlines what will happen if we continue in our rebellious ways -- we’ll get the smackdown.