If Hillary runs for re-election in 2006 and is beaten by Guiliani, she is essentially finished as a political player. She'll have all the political stroke that Al Gore and John Edwards have now.
Giuliani already announced he isnt running for Governor or Senator in 06. She is going to be reelected in a landslide in NY.
She definitely will run in '06. The fun will be in watching her declare that she will finish her term and not run for the presidency and absolutely no one will believe her.
Possibly, but Giuliani won't run against her -- for Governor, maybe.