Badly, but this isn't about feelings. It's a military decision. It's about saving lives in the long run with the Israelis having an obligation to protect all Israelis first.
Agreed, which is, again, why I ask where are the other Arab nations here? Will the help the Palestinians rebuild? Will they provide troops to keep the Israelis and Palestinians separated? Will it just go back to the same ol', same ol' with terrorism and rocket attacks? If the latter, then, from a military perspective, best to finish it now once and for all.
It appears so. Since the Arabs don't give a fuck, why should the Israelis leave a nest of terrorists alive next door to them.