Have you tried clicking on Add a new tab (the one with the plus sign) beside the existing tabs? Notes should be there. If not, do a search.
Notes do get published in the news feed even if you don't tag people in it. Right after you publish a note, go to the news feed homepage and click Most Recent and it should be there.The news feed displays Top News by default so that may be why you can't see your published notes there.
Hope that helps. :)