Hezbollah is a major part of the Lebanese government. Hezbollah controlled major chunks of Lebanese terroritory. If Lebanon was left out of this agreement, it would confirm to the world that it's a fake country unable to control its territory and therefore unable to complain when Israel enters it. Also, Lebanon has to enforce the ceasefire by containing Hezbollah {cue laughter} and preventing it from moving back south {cue more laughter}. And no, Lebanon will not be responsible and strong enough. If anything, Hezbollah will simply dress its fighters in Lebanese army uniforms and use Lebanese army equipment and move back south disguised as "the Lebanese army"
2) Remember that for Bibi, what's best for him is best for the country.