Sure. They have an urgency to eliminate Hamas, and they're unlikely to agree to any kind of agreement that doesn't involve Hamas leadership being removed, and I doubt the people of Gaza have any kind of ability or will to deliver them to the Israeli military.
Yes. That's the problem, and people in the west being antisemitic and supporting the terrorists doesn't make it better for anyone. It just makes Israel not listen to the west anymore, if it was up to the Israeli military there wouldn't be a Gaza anymore, USA UK and EU are literally the only thing holding back their military from just making a Glass Desert. The situation is so Tense that its basically not solvable with words. And using weapons will result in a gigantic humanitarian Desaster, worse than its already.