How can I project a clear light shape on the wall with an LED lamp?
Focusing the light requires some tinkering. The size of the hole is a factor. The distance between the light source and the apeture is another factor. Also, if you are using multiple LEDs then there will be multiple stars per hole; each LED will make a star.

Some words to google might be diffraction, interferance, and apeture. Also you could perhaps pick up some info from making an eclipse viewer.