The fact that Saddam was overthrown from without rather than within doesn't matter. Like many strongman dictators, he cultivated an air of invincibility; once he was overthrown, it sort of broke the illusion that the Arab dictators were invincible. Don't forget that even after Saddam got bitch-slapped in the first Gulf War, and was rebuffed in the Iran-Iraq War, he still remained in power. The second Gulf War showed that the dictatorships were not invulnerable. I'm not saying it's the only cause of the Arab Spring (as I didn't before), but I think it's definitely a part of it.
1979 is 30 years before 2010; 1990 is 20 years before it. Relations evolve. Saddam and Bashar al-Assad were friendly; their countries were not friendly, but not really enemies; for example, after Bashar al-Assad took power, Saddam stopped his accusations that Syria was smuggling soldiers across the border in order to destabilize and overthrow Iraq (Syria was probably never doing this, but Saddam's stopping the accusations indicates a new leaf in the relationship).
You're completely ignoring the internal political situations here. In Egypt, Anwar Sadat was assassinated shortly after signing the peace treaty with Israel. Saddam Hussein spent a lot of time and effort vilifying Israel (probably mostly to keep his people concentrated on an external enemy, distracting them from his own brutality). In fact, Saddam Hussein was probably the Arab leader who most strongly supported the Palestinian Liberation Organization in words and to some extent in deeds. For him to ally with Israel would be like North Korea declaring that they were going to ally with the United States against China. Maybe it makes sense in a very limited set of circumstances, but it's completely impossible.
As for nukes, Israel would have A. not trust Iraq to keep their word and B. believe in their own ability to stop Iraq from developing nukes regardless. After all, they did so OTL. Also in Syria. They also did a good job against Iran, though politics rendered the problem moot (without American interference in Israel's anti-Iran campaign, it's hard to say which way it would have gone; personally, I tend to believe that Israel would even have launched an airstrike against Iran if necessary, risking a proxy war with Syria and Hezbollah, though this is less of a concern if Syria is bogged down in a war against Iraq).