Can the arduino actually control outputs that fast, or are there bottlenecks somewhere? Like say for example you had an led or other component that could actually operate that fast, could you actually turn it on for 3 microseconds and back off? Or accurately change the duration a millionth of a second at a time (like from 31 microseconds to 32 microseconds).
Yes, and with just a $6 avr chip. Welcome to the world of embedded microcontrollers. Drop down to assembly language and you could probably write a simple loop that could toggle a digital output pin on and off at around or less then 200 nano seconds!
Lefty