I added a staff note,via the moderator wrench to a post. Then to a second post.
Now it seems that in all my posts (disregarding the topic) i see near my username the staff notes icon. I thought i added the note only to that post, and not to my user.
For me it feels a little weird to have the icon always there near my username. I expected to have the icon only at those posts for which i added the note(s).
Yes, this is normal. Staff notes are designed to be primarily attached to ‘users’ rather than ‘posts’. If you want to have staff-only information about specific posts, maybe whispers would be more suitable: