i don't understand a lot of this computer "stuff."
Sorry but I can tell from your questions.
The ATMEGA328 specs say it can sample at 20MHz
No it can't that is the clock maximum speed not the sampling rate. And an arduino only runs at 16 MHz.
PhotoDiode sensor with a max output of 17MHz and min of 12.5kHz depending on the setting
That is probably the rate at which it CAN be used at not what it WILL be used at, the actual frequency you get out depends on how fast the light is flickering.
analogRead function can only process at 10,000 samples/sec
Yes that is true for all arduinos.
or will it just store the input sample data until it can convert the data
No, I think you are misunderstanding the nature of electronics, what exactly do you want to do?