Is it possible to write notes to other PSN users or do they have to be friends first?
Welcome to the Playstation Community.
There are a number of ways to send someone a message/PM.
Directly on the PS3 or using this website, if they'e already a friend then it's easy, just choose them from the list, if they're not then yes, as suggested above you can use the "players met" list on the PS3, but that can be a bit of a pain to use scrolling through etc, if you know the name you can just type it in & if you got the name right it'll let you send them a message, lastly you can search for an ID on this website.
Customer Service - 1-800-345-SONY (7669)
Account & billing Support -1-877-971-SONY (7669)
Available Mon to Fri 8am - 8pm PST