Yes, you can apply for Green Card. GC processing time could be in years depending on the priority and your country of birth (Visa Bulletin For June 2012)
Your employer has to do the Green Card processing for you. I think, some other company too can file for GC.
I am not sure if GC can be applied for a person on L2 status - please have this checked with some immigration attorney.
You will find most of the info regarding Green Card from the following links.
[USCIS - Green Card](http://www.uscis.gov/greencard)