In my fourth year of my PhD on schizophrenia and I'm currently writing up my thesis. I'm procrastinating right now so thought I'd do something useful with what I've been studying.
And no, schizophrenia is not multiple personality disorder.
Edit: I have to get dinner and run some errands. I'm really enjoying this so I will definitely get back and answer the rest of the questions.
I think the reason that this advice is repeated so often is because so many people who just have run-of-the-mill anxiety tend to perceive themselves as "losing their mind" and start attributing relatively common things (like seeing/hearing things just before falling asleep) to schizophrenia. It's not that people with schizophrenia can't tell they have it, it's that so many people who think that they do are really just catastrophizing. Statistically speaking, if you think that you have schizophrenia, you almost certainly just have anxiety. You should see a therapist/psychiatrist either way though.
Oh yeah for sure. Diagnosing yourself with anything like that over the internet is asking for trouble.