Brake pedal vibration

Okay, you are saying the pedal vibrates when you try to stop the car? And is it only the pedal and not the steering wheel or vibration in the seat? If so, it sounds like the ABS system is activating at low speed when it shouldn't be. That will cause a vibration and sometimes a buzzing sound as the system engages. The issue then is tracking down what is turning on the system as it can be any of the 4-wheel speed sensors. About the easiest way to find out would be to use a scan tool and watch the wheel speeds reported as live data, what you are looking for would be one sensor that is reading much slower or zero compared to the other tires. So, say you are moving at 20 kph and slow down, you see all 4 at 10 kph, but suddenly the left rear reads zero, that would mean it is dropping out. As such the ABS system thinks that tire is now sliding and it will activate in order to allow the tire to start rolling again, but with a bad sensor or harness the signal doesn't change and it stays on.
Really there is no other way to find which one is failing unless you have an oscilloscope and the data for a good sensor.

The way the ABS system operates is by reading the wheel speeds at each corner of the car. If it thinks one is moving slower it activates. This will not turn on the ABS light or set an error code, as the system is working as it should. A common cause for this is a dirty connection in the harness or rust or other issue with the sensor itself which makes the signal weak. They work by generating a small voltage and sine wave signal as the tire rotates, it's just that one corner is generating a weaker signal. Sort of like having two lights, one with new batteries the other with worn out ones. Both still work so there is no error, but one has a bright light, the other dim.
In this case the computer can see the signals from both sensors, but the dim one fades out very fast. The ABS system suddenly thinks that one tire is sliding and activates.
Because they are all still working there is no error as there would be if the wires were broken or shorted, both of those would result in no signal and the system would see that and the light would come on.

From the second part you answered for the other question, did this brake pedal issue start at the same time or after the sensor you replaced? It's possible that the car needs a recalibration if it did as many times the control systems will learn and save the values of each sensor and a sudden change can cause odd symptoms.

It will take using a scan tool to watch the speeds from each of the wheel speed sensors, I suspect that one of them is reading differently than the rest. It doesn't need to be much, just enough to make the ABS unit think a tire is sliding even a small amount. I've seen it caused by a bad speed sensor on one of the wheels, or corrosion under a sensor or other corrosion in connections. The first thing is to use a dealer level scan tool and watch the reported speeds at all 4 tires.