Backgroundcolor of entire ToolTip

The problem is that all you're really doing is setting the CONTENT of the tooltip, not the tooltip itself.

So you'll need to style the tooltip to make this happen. There are some ways to do it with resources as seen in this post:

WPF- Changing Tooltip background to Transparent

or you can change your code to wrap that grid with an explicit ToolTip and set its background property:

<Image.ToolTip>
    <ToolTip Background="Black">
        <Grid>
            ...
        </Grid>
    </ToolTip>
</Image.ToolTip>