No
Yes, to get the bamboo blade there is a cheat to play zen mode once, then change the date in "Settings" to tomorrow. Then play again and do the same. Since you are supposed to play five zen mode...
Yes. And slicing it awards an Open Feint achievement. Also, it gives you 50 points!
for ninja chop chop you need 3 dragon fruits
There is an extremely rare fruit called the dragon fruit that is worth 50 points.