For the eraser, I believe you have to check what brush you are on. Some of them "fade" so it takes other things off as well.

I always clone stamp the picture on and then erase it using the "art history brush", but I think the normal eraser tool works fine as well.

For transparent, I usually use the "Opacity". I think there may be another, better way, but I can't remember.

For "Effects" I always right click on the layer and go to "Blending Options". I hope this is what you are talking about.

Other than that I'm not sure. I'm talking from experience on "Adobe Photoshop 7.0" though, not Elements. I would imagine the tools would be much the same though. Good luck!