During closing statements the lawyers are free to argue that the evidence should be interpreted a certain way, but you are basically correct that the jury should use their own judgment based on the facts presented. Yes, a persuasive lawyer is worth a lot!
As to point 2, there are exceptions and nuances, but basically the parties CANNOT present things that are not admissible evidence. During opening arguments the parties can use items that will eventually be admitted into evidence, and the email is definitely one of those things. The parties have already argued extensively over whether the email should be admitted, and the judge has ruled that it will. Ideally, the jury never hears or sees anything that is not admissible evidence.