A BLDC motor is actually a multiphase AC motor. The DC is with regard to the power supply, which is DC. The driver electronics set up a (usually) 3 phase AC system between driver and motor to drive the AC motor. Basically, a BLDC system consists of a inverter system and a motor. The inverter system in this case is basically three synchronized PWM sine generators or similar. In the tutorial, three H-Bridges made from two FETs each are chosen to apply the PWM signal to the three motor phases.
With regard to your Q2, there are diodes in parallel to the FETs, not capacitors. See this diagram. It is the same in the video at 4:08. These diodes are there to protect the FETs from the inducted voltage in the motor coils when turning of the coil current.
To transfer any amount of useable power, you have to make a AC system that is synchronous with the rotation of the motor. A sensorless system just starts with an arbitrary speed. If the motor does not need significant power output, it will start spinning asynchronously, producing next to no torque. At some rotational speed, inducted voltages from the motor can be interpreted by the controller, setting up a synchronous system, now producing plenty power.
A sensored motor makes its position measurable to the controller. In this case, the controller can set up a synchronous field from the get-go, having torque at startup.
This is relevant for some power applications.
In an airplane or boat, there is no resting torque, the propeller can spin more or less freely at startup. No need for sensors here: just spin the motor up, eventually get a reading, get power going.
In a wheeled vehicle, be it pedelec or RC truck, the motor has to provide a starting torque to get to any kind of speed. So in these cases, sensored motors are chosen.