1. It currently does not add them unless you click on a color somewhere. I agree that it should though, so I'll verify that we have this logged.
2. The color are not automatically removed from the palette, by design. The collection of colors remains with the document and as there is no way to know if the color is to be deleted for now, or only for the next few mins, we decided to leave them in. That said, it's easy to remove the colors from the document palette by selecting the flyout from the top of the palette and selecting Palette>Reset....this will purge unused colors.
3. I've heard this before and we have it logged as a suggestion.
If you decide to shut off automatic update It's very easy to add colors to the document palette....if you grab a bunch of objects and click and drag them to the palette it will add the colors used in those objects into the palette. I wonder if this is a better workflow given that you like to experiment with colors a lot.
T.