#2 is the big deal. Hamas (quite reasonably) thought they'd get more support. Other than thr Jew-hating Western left, they really haven't so far.

It was rational for Hamas to launch this war, as Israel was getting close to normalizing relations with many Arab states. Hamas will succeed in stopping that temporarily. But if Israel continues to  use violence against them the cost will likely be the destruction of Hamas.

The most important thing for Israel to do is to not succumb to ceasefire pressure and actually finish the job. Tens of thousands of Hamas and Hamas supporters need to be killed, and the infrastructure of Gaza needs to be destroyed. And all this needs to happen with minimal IDF casualties, which means they should not risk IDF lives for Gazan lives.