I think you misunderstand what "controlling by voltage or current" means.
The motor, as a matter of fact, is always controlled by voltage, a bit like a car is controlled by fuel injection. In the case of a BLDC, we usually talk of a modulated voltage generated by a voltage source (let's say 24V).
And although it is true that voltage is associated to speed, voltage induces current, and current relates to torque. What you usually need to control at your lowest level is current (or almost directly torque).
Controlling current "directly" may mean to switch the voltage measuring current and comparing it to a setpoint. Have a look at keywords such as DTC (direct torque control). This method is harder to master, and more complex to understand and implement, but it usually results in better performance.
A simpler, more intuitive way of controlling the motor is by making use of a standard PI controller, employing the Direct-quadrature transformations to transform 3-phases (I assume) currents into quasi-linear currents Iq and Id, where controlling Iq has a direct influence on torque, while Id should be kept at 0 as it's associated to energy losses.
Back-emf should be compensated for a good torque control.
Frequency goes up with velocity... Careful, because with it, also disturbances get more nasty.
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: -
Best Answer
No, the motor is behaving perfectly normally. If you want to measure back EMF in this manner, you can only do it during those periods in which no excitation is being applied to the motor.
Given this restriction, you can actually measure the back EMF on any of the windings.