Why Kill the Russian President?

Well, I hope someone answers your question Deez, as I was wondering the same thing.

I think, again, I think, that she was supposed to kill him so the Russians would think that an American did, so they would go to war or something. And Salt was indeed supposed to kill him, because when Liev Schreiber's character saw on tv that the Russian president didn't die, he got surprised and figured out that she was not following the plan, I mean, what she had to do. When Salt didn't kill the president, she already had changed her mind and was not going to do what she was trained for her entire life. And I guess that she did that because she never really wanted that life and because she really loved her German husband. So, I think that's it, but I might be mistaken.

She had to kill him to find Orlov and, more importantly, her husband. Because that's the only thing that matters to her in the first part of the movie and that's the only reason why she's doing what she's doing but if you look closely, you'll see she's actually not killing anybody.

The reason to kill the russian president was to put Orlov's ally as the new president.
Also to infuriate the russian people.

That way they could ensure that the necessary troop movements and missile deployment happened to encourage the US president to activate their nuclear arsenal which was needed for the nuke Theran and Mecca to push the moslems into a all out holy war to destroy the US part of their plan.

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They were setting up America. By killing the Russian President, American CIA would be blamed by the Russians. Then if their second plan succeeded and they destroyed Mecca and .... then the whole world would be against them.