ESC #1 smoked and burned. Really no need to spend time on it. It is dead.
FYI: PPM is a receiver signal protocol. PWM can mean either a receiver or ESC signal protocol. ESCs don't use PPM but this is not an issue for you.
You can calibrate and test with
[email protected] and it will work fine, but when you try to fly it, it will oscillate. If you successfully calibrated to 1000-1900 using
[email protected] you do not need to recalibrate. Just change to PwmSync or
[email protected]You should start by using a current limited power supply / light bulb for safety (so a bad ESC/motor doesn't fry yet another motor/ESC) and getting all your ESCs and motors tested and working. It's hard to do a setup from scratch without working ESCs and motors. Direcly connect the ESC to the RC receiver if you suspect the FC may be bad.
Run LibrePilot setup from the beginning and choose RapidESC from what I recall. After running setup, you can look at the Output page and verify that you have
[email protected] or PwmSync for all motors.
Having very different ESCs or motors won't stop you from setting it up. Having different ESCs or slightly different motors can cause slight bobbles when flying though. Unless they are very different (like KV1000 and KV1500) you should at least be able to get it to hover well and start testing moving around. You haven't got nearly that far yet.
Have you ever connected more than 5 volts to the FC? I know it says it can take more, but for instance the signals going into the FC can never be higher than 5 volts.
ESC firmware, that is a whole 'nother big topic. There are gadgets to buy to flash the firmware. No need to spend more than $5 or so but there is a lot for sale for more than that. There are two main brands of firmware (SimonK and BLHeli). There are two main processor (CPU) types and different ways (adapter cables) of connecting to them. Maybe research BLHeliSuite. Also (be aware that you don't need an ESC protocol faster than
[email protected], but that is a HOTLY contested subject):
https://oscarliang.com/esc-firmware-protocols/<soapbox>
For a middle of the road quad motor you are probably running say 6000 RPM at hover. That is 100 revs per second and with
[email protected] you are sending "change RPM" commands about 500 times per second. So even with
[email protected] you are changing the RPM 5 times per prop revolution. Smaller quads and higher RPM motors and full throttle might be 30000 RPM is 500 RPS and you can change the RPM once per revolution. Now I will tell you that ESC firmware smooths out the input variances which reduces the effective signal rate, but that is an issue to be addressed in the firmware if you think you actually need to change the speed of the prop 5 times in one revolution. You have to remove the smoothing to get the faster protocols working faster too.
It's not very useful to decrease the control delay from .002 to .000000001 when the human adds .25 to the delay. To actually significantly change the RPM several times per prop revolution would require huge current draws and generate torque that would snap a quad's prop and even snap it's arms off. Maybe faster response will be more useful in the future with much better hardware and autonomous control that takes the human out of the loop so that the quad is flying stunts itself.
I will grant you that there are high end cases where one step up in protocol speed (say 8x) is useful today, and that changing to a bidirectional digital signal format is useful, but claiming to need to change the RPM 150 times per revolution even in this worst case (that would be 750 times per revolution in a more normal case)? Or the other side: Reducing a typical delay from 1/5 prop revolution to 1/750 prop revolution.
</soapbox>