"Blue Hawaii" is a popular kakigori flavor which gets its name from an alcoholic beverage. The booze version usually consists of rum, pineapple, Curaçao citrus fruit, and some pointless blue dye. When you order a "Blue Hawaii" kakigori in Japan, it’s supposed to be pineapple/coconut flavored, but really you could be getting any damn thing with some blue food coloring thrown in. I think it’s safest to just say it’s "blue flavored."
Shiromitsu, literally “white syrup” is a translucent syrup made out of white sugar.
Oh, and “kakigori” is a Japanese shaved ice dessert, very similar to a snow cone, flavored with syrup and condensed milk.
I hope this has information has helped bring you one step closer towards complete enlightenment.