Confronting the Contradictions in 1 Samuel 17:54-58

There are several apparent contradictions in 1 Samuel 17:54-58:

1. Why would David take the head of Goliath to Jerusalem, which was at least 50 miles away, when Jerusalem was not the capitol of Israel at the time David defeated Goliath?

2. If David took the head of Goliath to Jerusalem in verse 54, why does he still have it when he appears before Saul and Abner in verse 57?

3. Why would David have a tent at the battle site in verse 54 when clearly he is living with his father Jesse in Bethlehem, going back and forth between Bethlehem and the battle site in verse 15?

4. Why does Saul seemingly still not know who David is, asking Abner whose son David is in verses 55-56, when he has had at least two extended interactions with him (16:17-23 and 17:31-39)?