Electromagnets have long been employed in DC motors.
Series and Shunt wound motors use electro-magnets rather than permanent magnets. Compund motos rely on both permanent and electromagnets together working with the armature. Even in a simple motor, the permanent magnets interact with the electromagnet of the armature.
AC motors almost always rely on electro-magnets.
Brushless motors are a new technology that I’m less familiar with. I believe you could make them with permanent magnets, but I believe most are made with electromagnets only.
You find them in you disk drives, CD’s, anything you need
They don’t wear out like brushed DC motors. My electric bike is made by Currie who was the first ebike maker to go to brushless DC motors. They regulate power by varying the widths of the pulses (Pulse Width Modulation or PWM). Brushed DC motors have narrower rpm window than brushed DC motors which in turn is narrower than AC motors. An AC motors works at its best efficiency when receiving sine wave input, so if you generate it from battery, you need more sophisticated electronics than the train of square wave pulses used with brushless DC.
They are the newest approach in electric bikes because you can efficiently regulate RPM since you generally control brushed dc speed by an inefficient resistive load. Also you don’t need to worry about replacing brushes every 5000-10000miles. The down side is you need microprocessor based technology to control the pulses. And power electronics are about the least reliable semiconductors, so you do take a reliability hit.
Other than small frictional losses associated with the brushes, a brushed DC motor ought not be more efficient than a brushless DC or an AC motor. The brushless DC motors and AC motors are more powerful per pound than brushed motors with permanent magnets, and on a mobile platform weight savings is of benefit.
The hub motor approach used by Wavecrest is one of the more efficient electric drive train approaches being used and has the benefit of also not adding resistance when the electric drive is not in use.
As for what you do when once the batteries are dead, you recharge or pedal. Pedalling a 60 lb bike is not desirable, but it isn't incomprehensibly difficult. I've frequently traveled 15 miles after the batteries are dead. Some manufactures have portable solar chargers. Sanyo and Rabbittools have regenerative braking systems, so the rider could recharge the batteries back by pedaling if they used that technology.
I’ve never seen anybody put a battery in the front hub. Seems in a military setting, you might want the battery on the frame where most other ebike makers put them so you could quickly discard an 8-12 lb dead battery if circumstances called for less weight or change out a battery pack.