"Act / fact / ax / factual" all have short and sharp 'a' sounds. "Park" is a longer 'ahh' sound, and in Australia we totally drop the 'r' consonant and make the vowel longer.
It's common when learning English to accidentally say the occasional swear-word. I'm currently getting one friend to pronounce "can't" as "cah-ahnt" since her short Korean vowels could be misunderstood. :P
One thing to remember about swearing in English is that it's punchy and short, to add to its aggression. The short 'a' in 'fact' is too squeaky and high to sound like 'f*ck'. If I heard "fack" then I'd start laughing a lot! The vowel in 'f*ck' is deeper down, in the throat or even the chest.
By the way Romulus, "ax" is an acceptable American spelling for "axe". :)