Your title is confusing: ...checked fuel pump, pushed on relay and horn honks. That makes it sound like the FP relay operates the horn. Perhaps you were actually pushing the horn relay contacts??
Now that you know the pump runs, but not by pushing the FP relay contacts (you are sure?) then there is either a wiring or ground problem to the pump, or there is no power available at the relay. With the relay cover off, do you see the contacts close while cranking, then open again when you stop cranking the engine? If so, the ECU is doing its job. Now use a DVM to probe the two contacts of the pump relay relative to grounded metal. One should have 12V or so at all times. The other should only have 12V when the contacts are touching. If that one does, then somehow the current is not getting to the pump. Be sure to check the brown (ground) wire at the pump connector for low resistance to grounded metal.
Now that you know the pump runs, but not by pushing the FP relay contacts (you are sure?) then there is either a wiring or ground problem to the pump, or there is no power available at the relay. With the relay cover off, do you see the contacts close while cranking, then open again when you stop cranking the engine? If so, the ECU is doing its job. Now use a DVM to probe the two contacts of the pump relay relative to grounded metal. One should have 12V or so at all times. The other should only have 12V when the contacts are touching. If that one does, then somehow the current is not getting to the pump. Be sure to check the brown (ground) wire at the pump connector for low resistance to grounded metal.