How can educators address current events, against the overwhelming backdrop of media coverage on Israeli military action?

A central issue is Pidyon Shevuyim in Jewish tradition, in Israel, as well as in International Law.
Questions and related materials from 2000 can be found at http://www.jafi.org.il/education/news/mias/campain.html .

1. In Jewish Law and practice, Pidyon Shevuyim exemplifies the high value that Judaism places on the preservation of human life, provided that it does not lead to extortion, and the tradition of redeeming captives is an honored one.
2. Another value is mutual support and friendship, Kol Yisrael Areivim and to explain what it means and how the two relate, please see this discussion activity. The Israel website for the MIAs also offers some excellent quotations and insights.
3. The Israeli government authorizes action to seek our Missing in Action in the field and simultaneously reached out for diplomatic avenues to bring them home. It views the prime responsibility for the abducted men's safety as that of the  Palestinian Authority and the Lebanese government, whom it holds responsible for actions undertaken by organizations operating on its territory; it also holds the Syrian and Iranian governments responsible, as sponsors of Hizbullah and terrorism in Lebanon.
   These kidnapped soldiers were abducted by illegal terrorist organizations from sovereign Israeli territory and Israel asserts this as an illegal act of terrorism, and an infringement of sovereignty. These organizations cannot therefore claim the right to take "Prisoners of War". The Red Cross record in relation to Israel is a sensitive issue. Since Israel's recent acceptance into the International Red Cross, it is to be hoped that their response will be one of integrity and motivation to assist our MIAs. Certainly, this represents an important focus of campaign work http://www.icrc.org/eng  or http://www.cicr.org/eng/icrc
4. We uploaded a prayer composed by the Israeli Sephardi Chief Rabbi, Shlomo Moshe Amar for the Safety and Health of Gilad Shalit. Please say this prayer for all the kidnapped soldiers and add: Ehud Goldwasser 31, of Nahariya; Eldad Regev, of Kiryat Motzkin.
   Prayer for the safety of the soldiers (pdf format - hebrew)
   Prayer for the safety of the soldiers (MS Word format -english)

   Jewish Names of the 3 Kidnapped Soldiers
   Gilad ben Aviva
   Ehud ben Malka
   Eldad ben Tova

The three Israeli soldiers were kidnapped from different regions: is there a connection?

Izz-adin-al Kassam, a Hamas faction, kidnapped Gilad Shalit; it was clear that they wanted to move him via Egypt into Hizbullah's hands in Lebanon, as a bargaining chip for the release of prisoners. They have not managed to do this; Hizbullah has been threatening kidnaps on Israel's border for some time, but upped the threats recently.

It is reasonable in retrospect to assume that there was some connection and quasi-coordinated decision by the various organizations to pursue a kidnapping policy, as there were several attempts in Judea and Samaria, including the kidnap-murder of Eliyahu Asheri the same day as Gilad was abducted. It does not seem entirely coincidental.

Hizbullah also supplies rocket technology to the Gaza Strip and is attempting to supply it to the West Bank. This includes the Katyushas that were fired on Ashkelon. This is also strong proof that the two organizations have been coordinating their tactics against Israel, and that this cooperation has been upgraded in recent months. 

Is there a difference between Hamas/Gaza and Hizbullah/Lebanon, in terms of Israel's position?

Hamas leads the Palestinian Authority Government; Hizbullah is also a legal party in the Lebanese Parliament, but the Lebanese Government is responsible for all of Lebanon and the deployment of official armed forces, as well as their absence on the border with Israel.
In both cases, Israel has withdrawn to recognized international borders - and therefore any attack or incursion from beyond this line constitutes an aggression against Israel. Neither the PA nor the Lebanese Government have attempted so far to restrain the terrorist organizations engaged in such acts. Israel holds them responsible for acts of terror, because there is a direct line of accountability in a vicious circle.

Syria pulled its troops out of Lebanon in response to international and UN pressure, but not its other forms of activity. Hizbullah is getting weapons supplies delivered to Beirut airport and the south by air and land via Damascus airport, which is the way- station for arms paid for and delivered from Iran. This goes on with the full knowledge and acquiescence of the Lebanese government. It's a bottomless pit, but the international community has a potential for significant influence.
The Lebanese picture differs from the Palestininan Authority in physical and political terms: the hinterland is larger and more complex. In diplomatic terms, Lebanon is also an actor on a larger stage, a signatory to international agreements, and therefore susceptible to international influence, especially as the UN has made clear statements about the border with Israel and the need to deploy in southern Lebanon.

The PA is far more densely populated than southern Lebanon; Kassams can be operated far more readily than Katyushas and the proximity to major cities was a main factor in Israel's decision to launch an air and ground strike against terrorists in the Gaza Strip, following weeks of intense missile attacks on Sderot, the western Negev, the kidnapping and finally the firing of Katyushas on Ashkelon. This, despite international sanctions against the Hamas government: but it is obvious that the weapons and finance continue through smuggling over the Egyptian border.

However, as the PA is not a sovereign state, and because Hamas and Hizbullah are not governments but terrorist organizations, the PA's actions (or inaction) and the acts of deliberate aggression by both terror organizations are not covered by the extremely outdated Geneva Convention.  

What options has Israel explored?

Israel's policy has been to protest and seek diplomatic resolution through international cooperation, following immense and deliberate provocation.

With tens of thousands of lives endangered by the escalating onslaught of missiles and the growing risk of further kidnappings, Israel was faced with a difficult decision on both occasions. Like any other country that is attacked from over its border day and night, there came a point where it sought a deterrent and appropriate action to reduce these threats.