If this is trapezoidal drive, you appear to be turning on the gate of one of the "off" phases. This may be due to the reverse transfer capacitance which is quite high with all of those MOSFETs in parallel, or possibly you are drawing enough current in your inductive current path on board board to pull down the source with respect to some of the gates.
I would start by reducing the value of the 10K pull down resistor on the gate to 1K and see if this improves your problem - this may work if it is the drain-to-gate capacitance turning the FET on. In any case, measure the gate voltage on the FETs during their off period with respect to the source.
Can I use a sensorless control of the motor, by sensing the back EMF even if the motor is spinning very low?
Technically, yes you can. However, in practice, it is not possible/difficult. The reason is that because the back emf voltage is so low, you need to amplify it (extra circuits) or work with low resolution data. Since the resolution is lowered, you get cogging because it becomes difficult to identify exact point of zero crossing. Also, back emf can't be lower than the noise in your system, you won't detect it.
How can I energize properly the phases of the BLDC motor, from standstill, if it is sensorless?
You will do an open-loop start-up sequence and hope that the motor catches up. Continue open-loop operation until a critical back emf speed is achieved.
Can I use the IMU for finding out how to spin the BLDC motor properly without counter rotations (meaning that I know when to commutate)?
IMU generally gives information about accelerations. So, you will integrate that to find the rotor positions. This operation will take some time and there will be calculation errors (You'd get cogging in BLDC motors). I'd say, this method would be more difficult than the back-emf method. IMU method is better for stepper motors. (Stepper motors + IMU = nice gimbal system)
How can I hold the motor standstill when reaching the setpoint?
You will switch the mosfets at a constant frequency. The motor will move at a constant speed. Is that what you mean by this question?
Should I implemebt a speed controller or a torque (current) one for such an application (sensorless driving of BLDC motors at low speeds)?
BLDC motors are inefficient and hard to control at low speeds. Why not use a stepper motor? If you really have to use BLDC, though, use both current and back emf method combined. They have their benefits.
Best Answer
If you have a scope available you can look at the input and determine if you have noise or if the problem is with your sense circuit. You could also try to add some capacitors on the input this might fix your problem if noise is the issue. You can also use an multimeter to determine if your current measurements are correct or you can invest in an VESC which can log power at both the input and output.