It's not complicated. Syncing Notes via iCloud is not a backup. It keeps Notes in sync across multiple devices and computers, and does so using the IMAP protocol which is why you need an iCloud email address to do it.
No, you're not going to lose contacts in iMessage. Yes, this is an iCloud email account.
For Notes to sync, Notes needs to be turned on in iCloud Settings on all devices connected to the same iCloud account.
You are right. With your instruction, I am able to see my notes on both iPhone and iPad now. Thank you very much.
Now l have another question. I can see my calender on both iPhone and iPad. But if I log in icloud.com, and click on the calendar icon, nothing shows up. why is that? How can I fix it? Thank you in advance.