Hamas and Hezbollah are essentially Iranian proxies. The Palestinians have received real support from Iran. It is becoming increasingly clear that war with Iran is a strategic necessity for Israel. Israel regardless of US and world opinion cannot leave Iran’s nuclear infrastructure intact, functional and unmolested.
Actually, No. Hamas and Hezbollah are two different entities and Often receive different support.
Hezbollah has been and still is very indigenous to Lebanon. Way before Iranians mullahs came along. Surprisingly or not, both Hamas & Hezbollah (under different banners, especially for the former) have been around in that specific region fighting Israel way before Iranian Mullahs came to power, or Iran's regime ever aided them; and at that Mostly Hezbollah since 1979 regime change in Iran.
Other than that, most Arabs consider Hamas (never mind Iranian mullahs) a terrorist grp, who make deals with Israel too. Hezbollah is a different ballgame and viewed legit (indigenous) in Lebanon, by most average Arabs.
Israel believes that Hamas is already resumed building new tunnels into Israel.
Well, Israel needs to look inside its own too, just as the U.S. and others do, regarding Hamas and terrorism.