Brake warning light turned on

This is normally caused by your brake fluid getting low. This could be either due to the pads getting worn out and it needs more brake fluid to extend them so it trip the fluid level sensor or there could be an actual issues. Either way, we need to check the brakes and make sure there are no leaks.

Basically we just need to remove the front and rear wheel and inspect the brakes. Once we know what they measure thickness wise and if there are any leaks then we can go from there.

https://www.2carpros.com/articles/how-to-replace-front-brake-pads-and-rotors-fwd

Welcome to 2CarPros.

What is the actual code that comes up? That would be the first thing to check and go from there as it would give some direction as to what the ECU thinks is wrong.

It is very possible that it is the module and that the used one is also bad. When you replaced it did you use the special pressure bleeding tool to complete the bleed procedure on it, if not it is possible there is still air in the system?
The booster usually won't cause the pedal to drop, it may cause a very hard pedal though.
The other item that could cause the pedal to go that far would be a bad master cylinder.

Okay, with that code you will need to connect up a scan tool that can read the actual pressure sensor output. Then read what it shows as you step on the brake. It could be just a bad sensor or harness. However, that shouldn't cause a pedal drop either, only that the system was disabled. The HECU is another item that could set this code but that can be tested using the same scan tool.

Hydraulic and Electronic Control Unit - This is the ABS/ESC control unit on your car. The vibrating and noise suggest it is activating, pedal feel during ABS is somewhat normal as the ABS has taken over the brakes and the pedal sort of feels like a sponge. That could be caused by a failing wheel speed sensor. However if the pressure sensor for the unit is shorted or isn't getting full voltage the HECU may activate as it thinks you are stepping on the pedal harder than you are.
Because 99% of the controls and sensor inputs are on the communications bus there are no tests with a meter or other simple tool that will show you what you need to know, only a scan tool will be able to read the data as the components "talk" between themselves.

It sounds like for the brake light is the front pads are worn down and it lowers the brake fluid in the reservoir causing the brake warning light to come on.

Here is a video and guide that will show you what you are in for when doing the front brakes:

https://youtu.be/7zjHSFVangI

and

https://www.2carpros.com/articles/how-to-replace-front-brake-pads-and-rotors-fwd

As far as the air bag light you will need to read the codes to see what come up. We are working on a video for that right now and will have it in a few days if you can wait that long.

Please let us know what happens.

Cheers, Ken