Most people don't know about the loopOut and loopIn expression methods...

This script will allow you to select one or more layers and create a solid, choose the color and place it directly below the footage layer and it will trim the in and out points of the new solid to match the footage duration.

"when I pre-compose a layer I sometimes want the layer to begin at the start of the new pre-composition and not maintain its original in-point."

If you want a property to animate on 2's or 4's like they do in cel animation.

The Difference Matte effect creates a transparency a mask or a matte by comparing the pixels in a source layer with the pixel in a defined difference layer, and then keying out (eliminating) pixels in the source layer that match both the position and color in the difference layer.

This will make your layer/object bounce along an imaginary 'floor'. Paste it into the 'position' attribute for your layer.