Peppermints are, shall we say, not a normal part of a meal. Like all mints, they have peculiar effects on the mouth, changing the taste of anything eaten after them, usually not for the better. And peppermint in particular tends to be associated pretty strongly with toothpaste.
You will sometimes encounter after-dinner mints, which are often mint-flavored (not peppermint-flavored) chocolates, but could be peppermint candies (the round ones with red stripes), or even, indeed, peppermint humbugs. However, as the name "after-dinner mint" implies, these are something eaten after the meal, as a sort of palate-cleanser or breath freshener.
That all said, the passage doesn't imply any particular reason for Harry leaving out the peppermints, and there isn't a cultural reference that you're missing or anything like that. Harry could have been putting off the peppermints for eating after dinner, or perhaps he was just a sensible boy who didn't like his food to taste like toothpaste. (Disclaimer: I hate all things mint in any use other than toothpaste. Mint chocolate chip ice cream, in particular, is a mortal sin in my book.)
Note that "humbug" as a type of candy is definitely a British term: on this side of the pond, we only use the word "humbug" in the "bah, humbug" sense.
Best Answer
In this case read it as adjective. An adventure park is a kind of theme park, like Disneyland.
Yes, "Adventure" can be read as a verb, meaning "engage in daring or risky activity" but it's not used like that in this case - this to should be read as to a location, not to perform an activity.