...some left for me.

1. Are there female dwarves?  If not, do they just find baby dwarves in the "rock patch" much like we were told about babies being found in cabbage patches?

a.  There are good answers below, but to expand, no more than a third of Dwarves are female, and not all of those marry, so Dwarves need very secure homes - population less being very hard to make up.  And yes, female Dwarves have beards.  Since we are told that few outsiders can tell male from female Dwarves, it's fun to wonder if any of the Dwarves we encounter are actually women.

2  Does Tolkien ever mention the stone-giants in any of his other works or letters?  (Over Hill and Under Hill)

a.  No.  For practical purposes Trolls seem to BE Stone Giants, but the identification is never made.  i like to say that such things in The Hobbit are the result of Bilbo's literary imagination.

3  Do the goblins take Bilbo and the dwarves under an extention of Moria?

a.  No.  They are at the 'High Pass' several hundred miles north of Moria.  Note that the Goblins had only recently opened a door on this pass.

4  Did Tolkien change his view on elves after the Hobbit?  Because I noticed that they way they act in LotR and the Sil are really different from the way they act in the Hobbit.  Or is it just that they are the Wood-elves?

a.  Most of the differences can be rationalized by calling Thranduil's people Wood-Elves - but note the Elves of Rivendell are a lot sillier in The Hobbit than in LoTR (in both works the Elves of Rivendell are first seen singing; compare the songs).  And it is hard to see LoTR Elves of any sort teasing travelers like the Elves do to the Dwarves in The Hobbit. Again, it's best to blame Bilbo's storytelling instincts. 
     By the way, it was Thranduil's father Oropher who founded the kingdom, and the underground palace in Mirkwood was built in imitation of Menegoroth, the capitol of Doriath.