The little seeds in kiwis should be fine, as they are REALLY small.
However, what I would worry about is sometimes they are a bit sour. You can get really sweet ones, but they're also a bit on a sour side.
Since no one really knows, you can try feeding a very small piece, and observe. But make sure you taste it first, to make sure it's sweet.
As Kelsey said, most store bought fruit juices have lots of sugar added. And don't forget preservatives as well. If you can find something that has no sugar, no preservatives, then it should be fine.
Not sure about mushrooms, especially since it's a fungus with spores, don't know how hedgies would react to eating them.