Sleep syrup, but this was in the book only. In the film, Katniss just got up and left when Peeta was sound asleep
Peeta knew that having romance in the Arena would give him and Katniss more supplies, more views in other words.
Haymitch is Katniss and Peeta's mentor. He trains them for the Hunger Games.
Haymitch's second instruction for Peeta and Katniss are to find water.
Katniss, Peeta, Gale, and Haymitch
He's always drunk.
Stay Alive
To make Peeta seem like a tough competitor.
Marry Peeta. (This is a Catching Fire answer, not sure if what you were looking for.)
Because he knows that Peeta is innocent enough - the nightlock was not his plan - and that Peeta will charm and win over the crowd with his charisma anyway.
There was only one victor other than Haymitch, Peeta and Katniss. His name is not specified, and he was dead before the series began.
The boy selected from The Hunger Games is, in the first book, Peeta Mellark, and in the second book, Haymitch Abernathy is selected, but Peeta Mellark volunteers.
If they ran towards, they would be in the middle of the blood bath. Very few people make it out of the blood bath alive.