I am thinking of building an Android app that fetches Notes and Reminders associated with an Apple ID. Is it possible to access them with http requests somehow? icloud.com uses their data, so I thought maybe it is exposed via some API, but I cannot find any documentation.
There is none. The only thing exposed so far is the CloudKit api which is for accessing key value data that you created yourself.
If you want to access reminders, then you can use the iOS native api: https://developer.apple.com/library/ios/documentation/DataManagement/Conceptual/EventKitProgGuide/ReadingAndWritingReminders/ReadingAndWritingReminders.html