I wanna try to help how to remember the "ふん" thing.
First, you have to remember the default ones; 1, 6, 8, 10
1 = いっぷん = ippun
6 = ろっぷん = roppun
8 = はっぷん = happun
10 = じゅっぷん = juppun
And then for the remaining; 2, 3, 4, 5, 7, 9.
For the number (in Japanese) that is ended by vowel, then it's followed by ふん (fun).
For the number (in Japanese) that is ended by consonant, then it's followed by ぷん (pun).
So, since 2, 5, 7, 9 are ended by vowel >> に (ni), ご (go), なな (nana), きゅう (kyuu), then it must be followed by ふん (fun).
2 = にふん (nifun)
5 = ごふん (gofun)
7 = ななふん (nanafun)
9 = きゅうふん (kyuufun)
And since 3 and 4 are ended by consonant >> さん (san), よん (yon), then it must be followed by ぷん (pun).
3 = さんぷん (sanpun)
4 = よんぷん (yonpun)
That's why "what minute" becomes "なんぷん". Since "what" is "なん (nan)" that is ended by consonant so it must be followed by ぷん (pun).
"IMHO"
P.S: sorry about my english :)