Is it obligatory to pay the full brokerage fee or only part of it to a broker whose mediation was bypassed and an agreement was reached directly with the owner after obtaining the owner's number from the broker's employees?

The broker is not entitled to full commission until his work is completed. However, if he begins the work but does not complete it due to your actions, then he is entitled to a customary wage (Ujrat al-Mithl). The broker showing you the house is considered a commencement of work, and he is entitled to a customary wage for the benefit he provided. This is unless the custom dictates that his work is completed merely by showing the house, in which case he is entitled to the full commission, which is half a month's rent.