A synchronious microprocessor's clock just controlls the fastest activity in the chip; there cannot be any controlled activity faster, which does not imply that there are noticeable activities at all at that speed, of half the speed, or 1/100 that speed.
It is in fact possible to lay-out assembly instructions to generate a very precise cyclical signal pattern. as this will have do be done in a loop, some care has to be taken to avoid "jitter", but I think it will be possible to generate any square wave you want with a precision of 1 us. This can be done by explicitly generating the code to be executed on the fly. Such technique (self modifying code!) is much easier on a processor where the instructions are executed from RAM in the first place; I have once written a similar program for the Parallax Propeller.
A better solution, if only square waves are to be considered, is using a hardware timer which can be programmed up to a precision of 62.5 ns (I think, or maybe 125 ns). You can easily out check this by using the Tone library!
However the tiny 16 bit timers now show a restriction in the other direction: it will be not possible to generate extreme LOW frequencies. A technique call "pre-scaling" must be used, which reduces the resolutions down to 64/16M = 4 us. And even at this resolution the lowest frequency generated is 1/(24u * 65,536) =1/(2 0.256) s = 2 Hz
I can tell you a lot of how timers work - and also the rest of the AVR hardware - and it's also in the datasheet
But what do you want to know exactly?? I think I made all relevant statements in my posting #2. There are typos in it, but I think it's not absolutely unreadable...