Aza,
You can set the blend mode of your text layer to “Difference.” This would make the text white when it was over black, and black when your picture is white (of course, it’ll also do all the shades inbetween. If you want more control, you can create a gradient layer behind your text and pre-compose it. That will give you options for controlling when the text changes color. You could also animate a gradient (use the ramp effect for a simple gradient, or the 4-color effect for more color control).
As for the shadows, is your text layer close enough to the layer below it to cast the shadow? If the text is too far away, the shadow will have dissolved by the time it “reaches” your layer.
Hope that helps,
Jacob