Today is Saturday.
The man, the owner of the car market, heard that the girls had wanted to build a tree house. He said, "If you could pull that off," which means to accomplish in spite of difficulties or obstacles, "just by yourselves, I would eat my hat." That is a phrase telling the kind of thing that one would do if a very unlikely event really happens.
The host of the restaurant saw Amelia and said,"Long time no see.Just come in and sit down here at the counter and chew the fat," which means to chat or gossip. Amelia told him they had been cleaning up the lot. He said,"That place is an eyesore." You describe a building or place as an eyesore when it is extremely ugly and you dislike it or disapprove of it.
But on the next Saturday, they got to the lot finding there was a sign showing the lot was on sale. They were upset and went to the restaurant hoping the ice-cream would make them feel better. However, Amelia looked down on her mouth, which means to be sad. The host said to them, "You girls really got the rug pulled out from under you." That means to suddenly take away important support from someone.