For switching applications like this, you can compare a MOSFET with a relay. The gate-source voltage (Vgs) is the coil, and the drain-source path is the switch. When Vgs is greater than a certain voltage (in your circuit this is 5V), the transistor shorts out the drain-source path. For N-channel MOSFETs like here, the drain-source voltage (Vds) cannot become more negative than ~1V, since there is an antiparallel diode "built in". The power stage for one motor looks like this:
For the low side it is simple. As the source is connected to ground, you can directly drive the gate with a square wave voltage. In many cases they directly use the output pin from their microcontroller.
The high side is trickier, because when that transistor conducts the source will be pulled to to the positive supply rail. But the transistor always needs a positive voltage between gate and source in order to conduct. What does that mean? If +Vb is the supply voltage, then the high side gate must be +Vb
+5V (!) The circuit that accomplishes this tricky part is called "high side driver" or "floating gate driver". There are chips that do this, but in many ESCs they use a discrete transistor circuit.
This is also the reason why I said that, in order to check if the high side transistor is controlled properly, you need to use two probes, one at the gate, and another one at the source, and subtract them on the scope. Then you want to see a nice 5V square wave. If not, then the driver could be damaged, or the transistor's gate could be damaged. In fact, you measured both voltages above. In your last post, you would have to subtract the second from the third trace (low side drain is connected to high side source).
But anyway, your pictures look strange. Where was your scope's ground clip connected to? It should always be the negative battery terminal (ground).
I cannot clearly identify what might be broken. You have negative voltage at the drain, which shouldn't be possible because of that diode I mentioned above. The transitions are much too slow as well. I would next check both transistors of this phase for good soldering, maybe you also have a cracked copper track on the PCB. And I would put the high side Vgs on the scope as explained above.I rather suspect the drive circuit of the high side transistor here, because the falling slope of your last two pictures is fast, which indicates that the low side transistor is switching well. If that proves to be the case, the good thing is that you don't have to replace the MOSFETs, but the bad thing: you need to dig deeper into that tricky floating gate driver.
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