The Question and Answer section for Ender’s Game is a great resource to ask questions, find answers, and discuss the novel.
Ender is promoted because he beat the game that couldn't be won. This is surprising because he's been at battle school for such a short period of time.
Gravity, lasers, and spacesuits all effect the way the battles are played out. Learning to utilize each of these tools to their best advantage leads to victory.
Please ask your questions separately.
Graff is accessing Ender's responses. He is testing him. The boy hitting Ender on the head ends up with a broken arm.