I have the 58 AF-1 and can confirm that when attached to the camera mine doesn't show the aperture that you have set in Av mode either. I'm no expert but as far as I'm aware, you would only want to see this when you have the flash off the camera as you need to tell the flash your aperture so that it can tell you the distance to use etc. When it is on the camera, the camera is already telling the flash what aperture you have set.
Therefore when my flash is NOT on the camera I can set things like aperture, ISO etc. Actually I think "set" is the wrong word, I am telling it what settings I have on my camera so that it can tell me what distance the flash should be from the subject to get the right exposure. I can configure those settings in all the different modes.
Side note: However, I haven't got my head around how TTL or Auto work when the flash is off the camera as I thought those modes all relied on them talking to eachother when the shot is taken. I need to figure that one out. Anyway, at least I can tell you that I am able to configure those settings in all modes when the flash is off the camera on mine.
EDIT: I found this which explains off camera TTL pretty well. http://www.f1point0.com/2008/07/22/the-nuts-and-bolts-of-off-camera-flash-part-3-ttl-wireless/
If I attach it to the camera then I cannot configure these things as the camera is automatically telling the flash what settings I have configured. The flash therefore just tells me the distance based on what my camera settings are.
As for randomly flashing - mine doesn't do that. That sounds odd.