In short, "fast" is an adjective and should go only with nouns like "a fast rabbit" and quickly is an adverb and goes with actions like "talking quickly" however people who speak American English tend to use fast as an adverb as well, so it just depends with whom you are speaking.

"I speak so fast." --- This is much better to hear. Remember, that fast pertains to the speed while the word quickly is about to time. Fast is an adjective. (Adjective- describe a person, animals or things). Quickly is an adverb. (Adverbs- typically distinct manner, time, place and answering such as HOW? Adverbs often end in -ly). For example, "He walks quickly" -- quickly modified the action word "Walks"