Nice! Sounds like an interesting TL. The first timeline I ever wrote was about George H.W. Bush putting Dick Cheney on the ticket in 1992, Bush winning, and then being assassinated, and President Cheney in 1995. So I know a little bit about Dick Cheney.
I had several questions for a timeline I am rewriting. The premise of this timeline was that Bush died on the night of January 13th, 2002 after choking on a pretzel. The most obvious outcome would be that Cheney would become president. Here's a list of things I am wondering about?
. Who would Cheney pick to be his VP
In my timeline, Cheney selected Donald Rumsfeld (needless to say, I was going for dystopia). However, if Cheney became POTUS in 2002, I could see him considering a list of people. I can't really see him choosing anyone in the Senate, because if he does, that's one less crucial Republican vote in a split Senate. Therefore, I think he would choose someone in the Cabinet. I could see him selecting Rumsfeld, but I could even see him choosing Colin Powell. Politically, he would shore up moderates and Independents for the Republican side, and he's extremely knowledgeable and experienced in foreign policy. IOW, he's a perfect Veep for President Cheney.
. If that person was someone in the cabinet, who would most likely replace that cabinet position.
Well, I suppose that depends. If Powell becomes Veep, I think Condolezza Rice would be his SecState replacement.
. Would any of the Bush cabinet choices be replaced by Cheney
Definitey not. Cheney would want to work off Bush's image, and TBH, I think Cheney would get along better with all the Cabinet members better than Bush ever did.
. Would we still get the Iraq war or some analogue, or does Cheney not have the Political Capital or Charisma to get it done.
Well, with Bush having laid the groundwork to prepare the public and the military for an invasion of Iraq, the War in Iraq undoubtedly occurs. Off the top of my head, I'm not sure how Cheney would handle the operation.
. How does the war on terror continue?
Probably the same as OTL.
. Does Cheney run for re-election in 2004?
Most likely. If Cheney became President after Bush was re-elected, I would say he wouldn't run for "re-election" in 2008. But before 2004, yes, I do believe Prez Cheney would run for re-election. That brings us back to Colin Powell, btw - Veep Powell on the ticket with Cheney would be an uber GOP ticket for 2004 which I could see winning in a massive landslide over whoever the Dems nominate.