Just thought I'd give my 2c, seeing as I've also got an AF and I also struggled to get it working when I first got it.
As mentioned, the AF has a protective feature to stop you putting your finger through the shutter curtain. In theory, when you take the back off, the mirror slaps up and the shutter opens. In practice, this only works a) when you have batteries in it, b) when you have fresh strong batteries in it, and c) if it's not borked like mine is.
There are also a lot of other mechanical (non-battery-dependent) interlocks, like you can't remove the lens with the mirror locked up (nor lock the mirror up without a lens), plus the usual you can't remove the back with the darkslide out.
At first mine made a sound like it was trying to pull up the mirror and open the shutter when I removed the back, at one point it got all interlocked and I couldn't remove the back nor release the shutter, I unscrewed the base and poked around until it worked again. Now it just doesn't open the shutter when I remove a back, but that's ok because I'm careful with it.
Once or twice, a year later, it started working 'properly' again, ie flipping the mirror and opening the shutter when I removed the back, but after a while it got all interlocked and wouldn't do anything, some combination of remove batteries, darkslides, and hitting it with my Kiev and it worked again. Not the best thing to happen out in the field, but works again now.
As for the AF, no you won't get AF with a non-AF lens. But you should at least get the focus confirm '>O<' marks with every lens (that's open wide, ie f/1.9-4) when you half-press the shutter. With a non-AF lens you'll only get spot-metering, you only get full-metering with AF lenses. There are custom-functions that you can turn the focus-confirm marks on and off, if you can't see them that may be the problem. I've got a manual for mine somewhere, if it's not on the Mamiya website then I must have gotten it from butkus.org.
Also, if there are those marks in the viewfinder, but you can't see them properly, check if you have a diopter installed in the eyepiece (I think you need at least something to get it work work properly, not sure though). The viewfinder blind is bright orange, activated by a little lever by the eyepiece, it should be obvious if that's down (the metering gets very confused when on a tripod without your eye sealing it dark, learn to love this blind).
An awful lot of electrons were terribly inconvenienced in the making of this post.
You may want to start a fresh thread, your issue is getting confused with the other problem on this ancient thread.
Originally Posted by oliverlott
Mark Barendt, Beaverton, OR
"We do not see things the way they are. We see things the way we are." Anaïs Nin