Electronic – What are the standard PWM output signals that a microcontroller should generate for 3 phase motor control

So, if I want the speed to remain at, say 3000rpm, and increase the thrust from, say 400g to 500g, I increase the current through the motor. I do this by increasing the PWM duty cycle. But, this means the speed will also increase from 3000rpm to a higher value, right? How can this be maintained then?

You would only want to increase the torque (thrust) if the mechanical load were threatening to slow the motor down - by increasing the PWM to counter that increase in load torque you are largely keeping the motor at constant speed. Remember a simple DC motor (even a brushless type) has a very clear torque-speed characteristic that means, for a given speed at a given torque, an increase in torque of \$x\$ will reduce the speed largely by \$x\$ also.

It's a not a perfectly linear relationship and changes entirely when field windings are implemented but it's fairly reliable: -

Since there was no motor connected, you know it had to be from 'shoot through' (high and low MOSFETs on simultaneously).

A bit of a guess- the driver chip you are using is a bootstrap type that cannot drive the top MOSFET on at 100%- switching is required to charge the power supply. While there is UVLO protection on the high-side driver, it's possible there is some sequence of operations that can leave the gates powered long enough to trip the overcurrent protection.

You can calculate whether the 10K will discharge the gate charge of the three particular MOSFETs you are using fast enough for the overcurrent trip to not operate. This may or may not be a problem in the application depending on the tolerance of the MOSFETs to such abuse.