1) How could Bod Dole beat Bill Clinton in 1996? I could be wrong, but i think Clinton was involved with Lewinsky at this point, so maybe if that comes out earlier...
Clinton's involvement with Monica Lewinsky was a result of the 1995 Federal Government shutdown. I think your best bet in this case is to have said shutdown go differently, or not happen. If Clinton capitulates rather than Gingrich or Dole doing so, it's going to make him and the Democrats look a lot weaker. Or, if Clinton gives in at the outset, this is further going to erode Democratic support for him (the whole reason behind the shutdown was Clinton's refusal to support cuts to Medicare, IIRC). The latter probably ends him a challenger to his left--Jesse Jackson.
2) What would the next four years look like under Dole?
The Dole-Kemp ticket's platform was pretty conservative, despite Dole's reputation as a more moderate Republican. I would expect more deregulation and earlier deregulation than what occurred in Clinton's second term, another massive tax cut (if not a flat tax being enacted), and bureaucracy reform. No balanced budget or budget surplus.
If Buchanan is given a prominent role in the administration, there's probably some goings on about immigration 'reform', as well as a curtailment of Free Trade (which the GOP actually came out against in 1994's midterms...though again, NAFTA was their baby in the first place, so I wouldn't be too sure about any of that).
3) Who challeneges him in 2000, and do they win?
Al Gore is heir apparent to the Democratic nomination, though I'm not sure he'll win that nomination. Without a sitting VP in the race, Paul Wellstone is much more likely to enter, as are some other candidates that didn't enter IOTL's race. John Kerry, Dick Gephardt, Bob Kerrey, Jeanne Shaheen, etc.
My money would be on Paul Wellstone leading the Democratic ticket. Will he beat Dole? My money is on 'maybe'. Depends on how popular Dole's political agenda unfolds, and if the GOP is able to hold on to Congress in '98.
4) What happens to Islamic Terrorism? Would 9/11 still happen?
Not sure, though I lean towards the idea that Dole, in fitting with the GOP air of the nineties, is going to be reluctant to commit American resources outside of the domestic economy. So it's a possibility, I suppose.