you put the VFD between the line voltage and the motor.
kinda. the actual definition of "Hertz" is how many cycles per second. so 50 hertz is 50 cycles per sec. for AC line voltage is a sine wave that goes from off, to positive voltage, back to off, negative voltage, back to off.
yes and no. as you continue to reduce the voltage it would eventually not have enough field strength to keep running at full speed, under load. the problem with it is, as you reduce voltage the current in the motor goes up to try to keep the field established. the higher current would eventually burnout the motor.
yes, different motors have different ranges of freq they will accept. but in general, the VFD has the capability to increase as well as decrease freq.