Faurisson was sentenced to jail for "denying the Holocaust" as you put it. Chomsky believed Faurisson had the right of free speech "even if Faurisson were to be a rabid anti-Semite and fanatic pro-Nazi" as Chomsky's statement said. Chomsky said to use his statement as wished, and it was put as the preface of a Faurisson book.

When people ask him about this Chomsky says he has signed hundreds of free speech petitions and free speech should not be removed just because he disagrees with the person, citing Thomas Jefferson. Some people believe in free speech, some think people with certain critical views of Nazi era nationality policy towards Jews should be jailed. In the USA, the free speech view tends to win, and this is where Chomsky is from.

Hezbollah has 12 MPs in the Lebanese parliament. It represents the interests of a section of Shia in Lebanon, many of whom were driven from their homes in Palestine in 1948 by Jewish settlers, and are now barred from returning home (whereas a Jew from anywhere in the world is allowed to settle in the West Bank).

The PFLP is "terrorist", Hamas is "terrorist", Hezbollah is "terrorist", the PLO is "terrorist", the DFLP is "terrorist" - anyone who fights back against Zionist (or sometimes American) aggression is labeled a "terrorist".

Hezbollah was formed because Israel invaded Lebanon and began killing Shia there (or letting their helpers do so in Sabra and Shatila). Hezbollah arose to defend the Shia from this foreign invasion.