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It's a good test case.
1 and 4 seem like the might be core renderer bugs. But I'll mention workarounds:
1. Add a bit of distance between the cube and plane or use a smaller ray epsilon
2. Use a transparent shader
3. I think is a feature request that we should expose the "reflection visibility"
It would be awesome if you could expose the reflection visibility as a new feature. Combined with being able to turn off the camera visibility it enables some brilliant visual effects to be created.
There is also the problem that on Cube 4 somehow the cube's internal shadow is changing the colour of the sphere. That may well be fixed if the cube was truly transparent via the core renderer fix.
Thanks for the testing. I think most of these should be fixed with the upcoming bug fix release which will have a "reflection visibility" option on the object. #1 We're still investigating.