1.  A Succah that was not made with the intention of using it for the Mitzvah is valid only if someone built it with the intention to use it for shade.  What I mean is like what the gentiles build for women, for important animals or shepherds in summer, for aristocrats or those who watch fields.  However, if it was built with any other intention it is invalid since it was not built for shade.  Therefore, if one digs a cavity in a pile and forms a Succah, it is not a Kosher Succah since this pile was not made for shade [and what he does after the fact is "it must be made and not from something which is already made"].  If one originally made 7x7 handbreadths of the pile for the Mitzvah of Succah then one later hallowed it out and completed it, then it is valid since the Sechach made from it is considered done with the intention of using for shade.  However, if one only piled one handbreadth for the intention of Succah or for shade then dug out a very large Succah from the pile, it is not valid unless one originally piles an area of 7x7 handbreadths.  If one dug out from two sides 4 cubits of space on each side in addition to 7x7 handbreadths of valid Sechach in the middle, even the middle 7x7 handbreadths is invalid since the Sechach becomes invalid from the walls at 4 cubits.  [One may not build the Sechach before one builds the walls.  However, if one built a handbreadth close to the Sechach beforehand, it is permitted to use it as Sechach before the other walls are built like the example of one who hallows out a pile.]