Can I copy and paste all keyframed parameters (settings and effects) from one layer to another in Adobe After Effects CS6 within a single composition?
If you go to the sequence window you can hit uu (that's double tapping the u key), to show all modified properties. Then copy all the keyframes and values (drag the cursor over the whole timeline area, including the I-beams for non-animating properties (the ones that are highlighted in blue) and copy. 



If you want to copy properties that are default for one layer on to another you could use ~ instead of uu, that will show all properties of the layer.

Note that there are some effects and properties that you can't copy, they're usually things that have a custom value, like the source layer for effects that use other layers, e.g. compound blur.