1 That is alot of water, you should be concerned
2 Usualy to a sump or a lower area properly prepared drainfield.
3 2x4 for verticle support ?
4 Your contract calls for it so yes. Insulated ducts are also good
6 wood must aclimitise to your house. The instaler should know how
long.

If the drains were doing their job you should be dry. Maybe grading
will help, but where is the water table level . You need to hire on
site independant pro advise , an architect or engineer. Calling your
building inspector would be a start , but hire another pro also.