You're worse than me, "Baby beheading defenders" ;)
Israel is not of one mind about Gaza. As you point out, populations of both Arabs and Jews have been growing quite a bit in the past 18 years. Some Israelis would like settlements back in Gaza (and never wanted them removed in the first place). The atrocities are being used as cover for those who disagreed with pulling out, or to silence those who disagree with the wall, etc.
HAMAS cannot exist without foreign support. Who exactly is supporting them, I don't know, but I assume they have some government support. Iran? Qatar? KSA? Russia? We know that Israel supports the PLO, why not some to Hamas under the table? Anyway, I feel many of your arguments break down because you treat Hamas as just a bunch of neighborhood fanatical Islamists/thugs who want to kill Jews. That's certainly how Netanyahu wanted everyone to believe. He didn't want anyone to believe they were a real threat because then he'd have to do something about it. Who knows what he believed. What we do know is that the attack was well-planned and executed.
Why the rush into Gaza? The money and support that was behind Hamas will just find, or create, another group. Israel couldn't have done a better job of helping them with that PR.
As I've wrote often, Israelis need to understand what happened first and THEN decide what to do. Otherwise, they may be following the agenda of Israelis that DO want Gazan land. I'm not saying that's true. Only possible.