pouring rain
In the book, a few days
They dry up the nearby water supply.
Katniss had not discussed her plan to fake being in love to get sponsors with Peeta so he thought Katniss's love was real.
Peeta fell in love with Katniss when they were young, and Katniss didn't return the feelings. Peeta was in love with Katniss before the story started, and Katniss began to like him back during the "cave scene" near the middle of the first novel.
he hide in the mud nest to the river after his leg was hurt in the firdt book.
(Spoiler Alert) If you are talking about while they were in the cave, it was because she wanted to go to the dinner to get the medicine Peeta needed. Peeta wasn't going to let her go and risk her life for him, so he needed to fall asleep.
Katniss did not inform Peeta that they needed to fake being in love for sponsors. Therefore, he thought the love was genuine.
Katniss showed loyalty to Peeta when she wouldn't leave him in the cave. He was injured and would be a burden to her, but she was loyal to him and helped him recover.
Katniss camouflages the opening of the cave by using branches, leaves, and moss to blend in with the surrounding environment. She uses her skills as a hunter to make the entrance look like a natural part of the rock face, effectively hiding it from view.
Katniss does not find out in Catching fire, but in the first book, when they are in the cave by the river.
Well, they are in there for quite sometime so they talked a lot more than jsut once as they waited for Peeta to heal, but Katniss told him the (edited story as not to get in trouble with the capitol since it involved illegal hunting) of the time she got Rue her goat. And Peeta told Katniss of the first time he saw her.
Katniss was very surprised, angry even. She didn't understand what he meant, she thought it was just to get more sponsors. Katniss pushes Peeta afterwards for announcing a lie, because she thought she looked like a weakling. Afterwards Haymitch says that it's a good thing because she will get sponsers, too. It would put on a good show, and that's exactly what Panem wants. At the end of the book, Katniss finds out that Peeta meant what he said, and it was the truth.