If a block contains no SegWit transactions, does a miner send an (empty) witness? Also, would that block's Coinbase contain some kind of empty witness commitment?
BIP141 only requires a commitment to the witness tree to be present when there is at least one segwit transaction (= a transaction that spends a witness output) in the block.

This means that old miners in theory can keep working after segwit activates, as long as they don't include segwit transactions (easy, as they are nonstandard to them) and don't build on top of invalid blocks (harder, as it requires an updated full node).