Israel hasn't really engaged in regime change. If anything the opposite. There was a single failed attempt to get the Christians into power in Lebanon. But mostly sort of the devil I know. We have Hussein in Jordan. We had Assad in Syria. Egypt had its own turmoils but not much Israeli involvement. The PA and Hamas were also viewed as a stabler alternative to chaos. Saudi and the emirates pretty stable. Turkey (not quite middle east but whatever) also have their internal turmoil. Iran has been stable as well.
This is true but that happened mostly after Hamas already took Gaza. Israel would have greatly preferred for the PA to control Gaza. The regime change in this case was done by the Palestinians themselves. The Israeli right wing did to some extent strengthen the division once it was in place. The Wikipedia article reads like a propaganda piece and I would not trust it at all. I've lived in Israel through this period so I have a pretty good first hand knowledge/experience of the events.
The PA didn't really come close to negotiating peace and given Hamas were not able to. See Hamas' suicide bombing campaign during the Oslo peace process. The PA, somewhat as a response to Israeli policy, decided to pursue trying to force Israel to yield via a combination of armed and political struggle and not negotiate with it. Strangely enough security cooperation did continue throughout (and the PA is basically supported by the IDF otherwise it would likely have been toppled). This all happened after the Oslo peace process collpased due to Hamas.
Bush pushed for an election as he wanted to have solved the middle east situation before his presidency was over, against both Israel and PAs wishes. Then Hamas won and Bush again pushed PA to do a coup which failed and PA was kicked out of Gaza.
