You can only ask one question at a time so I edited down accordingly.  Mushrooms are classified under the kingdom of fungi.  They are the spore-bearing portion of the fungus and have a few basic parts: the stem, the cap, and the gills on the underside.  These gills on the underside of the cap are thin sheets of tissue called lamellae.  They contain the spores and are used for spore dispersal.  These gills can be highly varied and are often used for species differentiation and identification.  It should be noted that not all mushrooms have gills; some have pores on their underside for spore dispersal.