I have DID, and have had some episodes of psychosis due to extreme stress (not dx'd schizophrenic though). An important distinction, like the posters above noted, is that in psychosis the voices seem to be coming from outside, whereas in DID the voices are within.

As for DID voices (alters, others, whatever you prefer) being mean, nasty, angry, etc....they absolutely can be all of that and more. They can also tell you to do things to yourself, or come out and do it themselves. This is often a form of protecting that has gone astray, or is no longer needed. An example of this is an alter that would SI, because someone talked (in therapy). This one had developed this as a protection so no one would talk, because any time they did, they would get hurt. The problem is that now it is okay to talk. There is also the possibility of an internalized perpetrator...one that acts just like an outside person from the past. They can be particularly nasty, but have a purpose (I don't know what it is, probably different for everyone), and over time, can learn to no longer be abusive.

As for the things you describe seeing...that could be due to schizophrenia, but it could also be due to DID. The seeing someone could be an other trying to present them self to you, it could also be a flashback. The incident with waking up and finding the writing and then being presented with an empty page once you got to the other room could be explained by an other changing their mind about sharing with you, or another other besides the one writing it deciding its not time for you to see it. It only takes a few seconds for one to come out, destroy some paper, and then pick-up a blank page...its possible for this to happen and you have no idea that it did.

When I had issues with psychosis, the things I was seeing were more of the "absolutely not possible" variety. I saw people that disappeared when I looked directly at them...but these people were about 10 inches tall with cat heads and wings! I'm sure it's possible to see realistic looking people with psychosis, but those weird things were my experience.