Counting in Japanese

I suppose English can be just as difficult, when I think about it.  Which words do you add "s" on the end to make it plural?  Which words remain the same in both singular and plural forms?  An ear of corn.  A bunch of bananas. 


In Japanese, it seems like every single thing has its own word for counting.  Usually you can get away with the generic counting words hitotsu, futatsu... (1 of something, 2 of something...) or ikko, nikko... (1 of something generally small, 2...).

This quiz was part of a handout at one of my schools.  How do you count each of these??


#1 - Tofu is counted as "chou" (丁), so one block of tofu is icchou.


#2 - One bowl of rice can be counted two ways, ichizen （１ぜん）or ippai
     （１ぱい）.


#3 - One squid (as food, not as an animal) can be either ippai or ippon (一本）.


#4 - One cabbage can be either ikko (as I mentioned above) or hitodama （１玉）.


#5 - A bunch of bananas is hitofusa （１ふさ） and one banana is ippon (same as  
       one squid).


#6 - One...I don't know...bunch? of somen noodles pre-cooking is either
       hitotaba （１束）or ichiwa （１わ）.


I think one of the hard parts is even just the number 1 has many ways of pronouncing it.  It can be ichi, or that can be blended into the following word (ippai, icchou).  It can also be added as "hito" from hitotsu.  How do you know which one to use??  Sometimes I can guess from just having been in a Japanese language environment for so long (kind of like how I can usually write a kanji in the correct stroke order even if I never wrote it before).  Other times....no clue!