Can iCloud notes be synced with different accounts? Is it possible to synchronize notes with different accounts? For example, if I write something in my notes - my friend will open his notes with his account and see the change.

Is this possible?
No, iCloud was not meant to work that way. 

Some third party Apps, though, will do exactly what you're looking for. AppCrawlr has got an interesting list, which might be worth looking at.