They only supporting Hizbollah because Israel is occupying Syrian territory... "the enemy of my enemy is my friend".. and Hizbollah only exists because Israel invaded and occupied Lebanon and still occupy disputed areas.
Actually, I think the only disputed territory is what Israel gained through taking the Golan Heights and it was disputed with Syria before that. Of course, that naturally means the dispute became a dispute between Lebanon and Israel, but still these are not territories Israel occupied in its invasions of Lebanon, but territories it has been occupying long before.
On an interesting side note, however, Israel did occupy Southern Lebanon back in the 1948 War.
And Iran only supports Hizbollah in many ways, because it is a thorn in Israel's side (same with Hamas) and happen to have the same political/religious ideas.
Iran established Hezbollah. It isn't just an alliance of convenience. With Syria this is the case as their favored group, Amal, is simply not as capable as Hezbollah.
Not unless they're certain they can win the war.
Israel can pretty much remove over 80% of the capabilities of the Syrian military within less than 12 hours, by utterly destroying its military bases.
It's not '67 anymore when the Syrians could even hope to stand a chance, the gaps between the capabilities of the two armies have increased exponentially during the years and the Syrian army is no more of a threat to the IDF than the Iraqi army was to the US military.
I think you are far too optimistic and have been bombarded with this absurd notion of Israeli superiority. Certainly Israel has been more successful against the crappy Egyptian and Syrian forces of the past, but that does not mean Israel is actually all that capable. Israel is simply better than the powers it has fought who are themselves not particularly good.
However, certain major strategic shifts are taking place that greatly imperil Israel's edge in conventional warfare. We saw in the 2006 Lebanon War how a capable military force can perform against Israel.
That is the result of Iranian training and as the Iranians have been building ties with Syria it is certain some of that training is being given to them as well.
One major change to the balance of power would be the possible purchase by Syria of the Yakhont anti-ship cruise missile. If Syria gets a few dozen of those it will be poised to sink every Israeli surface ship with ease. Such a development can hardly be taken lightly as you are taking it. Also, Syria learned from the 2006 Lebanon War and has built up its arsenal of anti-tank weapons.
It would be irresponsible for anyone in Israel to think they can easily defeat Syria.