It's impossible to destroy Hamas. Can you kill an ideology? Can you destroy someone who wants vengeance for their family members, before they've even picked up a gun? Can you destroy the idea of wanting to defend your land, wanting to reclaim the land of your ancestors?
That's long-term - in the short term how're they going to identify Hamas members? Some will have guns, fewer will have armour, most will just be ordinary citizens who'll go to live amongst their families. No one but the most crazy will go head on against a 300k+ fully militiriased army.
The only way to destroy Hamas is to kill every single Palestinian alive, because that's where the next iteration of Hamas will come from. Anyone that says 'destroy Hamas' knows this and is basically looking for a front excuse for genocide.
Israel will contend themselves with a land grab - but as always they're shooting themselves in the foot and being short sighted because the events over the next month or two will live long in the memories of Palestinians and the arab world for the next 30 years.
They're not an ideology, they are an organization - just like Al-Qaeda and ISIS were, both of which are now decimated because the US and its allies committed themselves to doing it.
As for the other point, they won't need to ask each Palestinian if they're a card carrying member of Hamas. They will simply kill anyone who shoots at them and continue gobbling up territory as they go. Once they secure the northern districts, they will gradually move further south. Members of Hamas will probably fight from tunnels and through suicide bombers (a previous Hamas tactic), but they won't be able to win if they are outgunned from each of land, air, and sea, with nowhere to run since Gaza is cut off.