Kiriyat
It's in fact far more complex that what you describe and I strongly urge readers to do their own research.
> Iran had a democratically elected government, but in the early 50s, the UK & US orchestrated a coup that ousted that government, since they wanted to nationalize their natural resources and kick foreign oil firms out of the country.
Iran had had a monarchy for 2500 years. Then, after a brief power struggle, Mohammed Mossadegh (previously appointed prime minister by the Shah himself) became a leader for two years. He did later win an election. Indeed, he was ousted by that coup and monarchy was restored.
> The U.S. the installed the King of Iran as their puppet dictator. The King was a close ally of Israel and Saudi Arabia as well.
Characterizing Reza Pahlavi as a dictator or a "close ally" of Israel is an exaggeration. He was a monarch - and a reluctant one at that.
> These forces are not occupying the territories, they're native to the land, but just ideologically align more with Iran than other countries in the region.
By these "forces", you must be referring to Hezbollah, the terrorist organization that killed over 300 peacekeeping forces in the Beirut bombing during the Lebanese civil war, or the Houthi rebels that played a major role in causing the ongoing the civil war in Yemen.
> Part of how Iran was able to attract their support was by positioning itself as the force to stand against Western abuses in the region, (including Israel).
Almost every Arab country in the region stands against Iran, to the point of covertly cooperating with Israel. Those who align with Iran are virtually all part of the Shia/Alawite religious minority.
You must have a very broad definition of "terrorism" if you consider Israeli military operations to be "terrorist acts". Iran sponsors an out-and-proud terrorist organization called Hezbollah. They've committed textbook terrorist attacks around the world.
> Right, but my point is that isn't nor really a one-sided thing. Israel does it too towards not only Iran, but its closest neighbors, they regularly threaten to "bomb Lebanon back to the stone age", as an example.
...as a response to legitimate threats made by Hezbollah in Lebanon. Don't forget that Hezbollah started and escalated the war in Lebanon in 2006. Israel does not threaten Egypt, or Jordan, or even Syria itself except for Hezbollah's presence therein.