1) I believe classic counterinsurgency doctrine does apply in the case of Israel. Although its particulars are endlessly mutable, war itself is universal. However, Israel suffers from a terrible case of strategic "cogntive dissonance" regarding Palestinian statehood which prevents it from successfully employing classic doctrine.

One of the essential requirements of classic counterinsurgency doctrine is that the local people be treated with respect, and their interests generally enhanced. Because one of Israel's strategic goals has been (and may still be) the settlement of land formerly occupied by Arab Palestinians by Israelis, this essential requirement cannot be complied with. Palestinians know that no matter how nice an Israeli may seem, ultimately their home is subject to demolition at any time. This fundamental opposition sets up a source of conflict that cannot be defused. Israel would seem to want land more than peace, although this may be realigning.

2) That depends on what you mean by "working." If a constant level of uncomfortable international bad press, continuing low level terrorist attacks and reprisals, with an expensive drain on military age manpower and money is working (keep in mind Israel maintains one of the better economies in its area) then yes. However, this strategy is unlikely to lead to peaceful coexistence or decisive conquest. Personally, I think it's essentially face saving by politicians who don't have the guts to fight or the will to enter real negotiations - they fight just hard enough to maintain the status quo ante.

3) Israel's mistake is in treating the exercise of military force as a coercive tool. Not that it cannot serve as such, but rather it has manifestly failed to coerce very many Palestinians of late. A quid pro quo approach to violence does not defeat your enemy in a small war - it merely helps your enemy's recruiting drives.

Tel Aviv ought to privately determine exactly which end state they are willing to live with as regards the Palestinian people (and the various armed and unarmed factions) and then make a measured judgment as to exactly what role force is to play in achieving that state. It seems most unlikely that any military would recommend the use of ### for tat retaliatory strikes as the best long term way to curb any insurgent or conventional force.