If I connect with my iPhone to a foreign wifi hotspot are my Notes in danger? Does it automatically transfer Notes on new connection? If I didn't open the Notes app, or even if I did open it, can a Wifi hotspot read it?
No, iPhone does not broadcast your entire phone contents in the clear.
Any iCloud data sent over the network is protected by HTTPS.
Not that it matters because of the previous statement, but if an iCloud sync happened to transfer some data at the time, this transfer would only be a delta updates; content which one party does not have, not the entire contents of iPhone notes.