There were a few wars that Israel fought in Lebanon: the Lebanese Civil War from 1981-1982, the Occupation of Southern Lebanon from 1982-2000, and the War Against Hezbollah in 2006.

The 1982 War of Lebanon, also called "Operation Peace for Galilee" by Israel, was fought between Israel and Lebanon when the former invaded the latter.

No, and that is true for both the first Lebanon war in 1982 as well as the more recent war in the summer of 2006. The issue of captured Israeli soldiers is always presented when negotiations are discussed.

YES. The two suicide bombings against the Israel Defense Forces' headquarters building in Tyre, Lebanon took place in 1982 and 1983, which was during Israel's intervention in the Lebanese Civil War. This intervention is commonly called the First Israel-Lebanon War in Pro-Israeli circles (in contrast to the War with Hezbollah in Lebanon in 2006, which is called the Second Israel-Lebanon War).

The purpose of the UN troops was to try to end the Lebanese Civil War.