I'm not sure how feasible this is, Sadat and Assad needed time to plan and arm. But, if everything is the same...
1) No, it wouldn't have changed. If anything, there are even more incentives to do this. The election and the Munich Olympics (the Israelis were needless to say, out for blood after that. Operation Wrath of God really relieved the administration, they thought it was going to be far worse, and the prevailing mood in the US and in Congress would have made them support far worse) made sure that any serious shift in the post Black September/Nasser policy, which was pro-Israel in a strategic sense for the first time, in the Middle East for Nixon had to wait until 1973, with the obvious crucial consequences. The Israelis have a nuclear arsenal and the Arabs are still relying off of Soviet arms. I'm pretty sure that Operation Nickel Grass goes on if the war plays out the same.
2) Yes. They were going to use the oil weapon the next time the region blew up, as Nixon well knew.
The big possible ATL changes come afterwards, as Nixon is a fully focused President at the height of his power and does not need to put up with Congressional bullshit as Ford did OTL. But it will be tough. Remember, Faisal cares about Jerusalem, not the Sinai, and I'm not sure Nixinger's preferred solution of a Vatican like status will satisfy them. With Egypt, it's vice versa. Syria cares about the Golan Heights. Israel cares about... not giving anything up. Tough, even without Watergate, and that blows up come April.
Congress and Nixon loathed each other by this point, well before Watergate. Nixon had one of the most dreadful relationships with Congress in history. But Congress is also dominated by the Democrats, which back then were the pro-Israel party. McGovern had committed himself to a stronger position with Israel than Nixon had, ironically enough. It would be tough to attack Nixon over the response, given that he already had a 60+ percent approval rating. Again, the danger is that Watergate still lurks. The question is can Richard Nixon get some important bridges built before he becomes a lame duck and Congress can destroy them?