How is 本 pronounced when after 二?
二本 ni-hon (two sticks)
It must be really easy to make puns in Japanese.
That reminded me of this thing in Dragonball Z / Kai. The blue guy in the small planet (don't remember his name) makes bad Japanese puns all the time (although I didn't understand them at the time).
And this is why kanji is really helpful ;)
本 is pronounced differently (pon, hon, bon) depending on how many (ippon, nihon, sanbon, etc). I dont quite remember all of them but its worth looking up.
Is 四本 really よんほん, or is it actually よんぼん?
よんほん. For 4, never add dakuten. e.g. 四匹（よんひき）、四階（よんかい）、四杯（よんはい）. An exception is 四分（よんぷん） which adds handakuten to the counter.
Do they really count chopsticks as individual sticks? I'd always "a pair" instead of "two".
I would suggest using 膳（ぜん）to count pairs - 一膳、二膳、三膳 etc.
Would this be two sticks or two pairs of sticks?
Is there a rule when to use "hon" to count something? Maybe something made of wood?
Something like a stick that is long
Hon is for anything long and cyldrical, sticks, bottles, tubes, etc.
本 is not only a book, it is a counter for long cylindrical objects.
This is a list of things it is used for:
counter for long cylindrical things; counter for films, TV shows, etc.; counter for goals, home runs, etc.; counter for telephone calls