I'm not super knowledgeable about Bitcoin's internal workings, so sorry if this is a silly question:
Could there exist a block whose hash is above the target for every possible value of the nonce? If so, what would happen? Would mining of new blocks just halt for 2 weeks until the difficulty adjusts the target to something above what is possible?
The merkle root changes everytime the transaction selection changes (or transaction order). The timestamp changes. The coinbase transaction changes the address(es) that is pays out to.
All the miners in the entire network aren't all working on the exact same block.