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? As the question title says. Is there a shortcut, or some way to do this?
Single composition suffices.

The only thing I found is to copy all effects, by selecting a layer → effects panel → CTRL + A to select all effects → CTRL + C to copy → Go to other layer → effects panel → CTRL + V to paste the effects.

The aforementioned process copies all effects and their keyframes, but not the individual settings. The settings of each effect is the default. That being said, I am surprised to see that they are actually keyframed.

Also, it doesn't copy other keyframed parameters (non-'effects'), such as Position, or Opacity.

Is there a way to copy all keyframed parameters exactly from one layer to another?

I'm working with Adobe After Effects CS6. Thank you.
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.