The Giver is the new name for the Receiver of Memory. He becomes the Giver when Jonas is selected as the new Receiver. Now he must give his memories to Jonas.
Sameness is the guiding principle of the society they live in. The idea is, as you might guess, that people should be pretty much the same as one another. They should not really have strong feelings and they should not feel close ties to anyone in particular. Everything that can be controlled will be in the society will be.
This includes the weather. They control the climate so they can have as much Sameness as possible.