LEDs with same current rating but different forward voltages
Yes this is fine.  LED's are more current than voltage sensitive (a switching current controller prevents thermal runaway without dissipating a large amount of power through an inline resistor) and placing elements in series ensures that the same current runs through them, as there is nowhere else for the current to go.  As long as you don't exceed the current rating for a significant period of time and cooling is adequate, the LEDs won't be damaged by rated current.

Your current controller will provide whatever voltage is necessary to the load to cause the set current to flow, within it's limits.  If it is a buck(step down) only controller, it can only provide voltage up to it's input voltage, and if it's a boost(step up) converter, it will provide the necessary output voltage up to the point where its input current hits max, so there will be a minimum input voltage that must be provided for a given load.  Paralleling LEDs with different Vf however requires individual control of each LED.  

As far as a resistor goes, think of it as a cheap high-safety, poor quality current controller.  Use them when input voltage is relatively steady and load current is very small compared to available power.  Switching controllers at higher current levels, for variable source voltage, or for variable control of the LEDs.