How fast does arduino process each line of code?

One other speed related question too. So I know arduino has a DelayMicroseconds command, and the reference page says it works accurately in the range of 3 milliseconds and up. Thats incredibly fast, 3 millionths of a second.

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).

Also say you have the most simplest photo flash type code of all, no delays, just a simple "when input #1 is high, make output #1 high". What sort of timeframe does it take for it to actually register the input and produce the output? Is it within the range of mere nanoseconds, or microseconds, or what?

Thanks.