Is the tenant entitled to refuse payment of the agreed-upon broker's fee due to the broker's breach of the agreement's terms and lying to the landlord, and the resulting material and psychological harm to the tenant?

The broker is not entitled to a fee unless the agreed-upon work is completed. If he does not fulfill the agreed-upon condition, such as pointing to an apartment that is to be received at a specific time and this does not materialize, then he is not entitled to anything.