1. The way Argumentative writing tries to convince the reader is appealing to solid evidences; and persuasive writing focuses more on the readers' emotional drive or inner perspective. (Thus the first one)
A claim is a statement or opinion about the truth of something, generally without presenting evidence of it; and a rebuttal is a claim disproving certain accusation, statement or certain argument. A rebuttal can also be the evidence provided to dispute or deny a previous presented evidence.
Therefore:
2. "Effective argumentation anticipates an opponent's rebuttal".
and
3. A claim is "a statement that takes a clear stand on an issue".