Is Hezbollah a terrorist organisation? I didn’t think so.
Yes, of course, why would you not think so?
Either the entire organization or only its military wing has been designated a terrorist organization by several countries, including by the European Union and, since 2017, also by most member states of the Arab League, with two exceptions – Lebanon, where Hezbollah is the most powerful political party, and Iraq.
Here is a list of countries and groups of countries that defines them as a terrorist organization:
Arab League, Gulf Cooperation Council, Argentina, Australia, Bahrain, Canada, Colombia, Germany, Honduras, Israel, Malaysia, Paraguay, Saudi Arabia, United Arab Emirates, United Kingdom, United States
So the answer is a resounding yes.
Yemen war is a big conflict and all, but I wouldn’t call it terrorism.
Again, some countries disagree with you. But more important is that the UN sanctions them and forbids arms transfer to them, which Iran does in violation of International law (recently a weapons shipment from Iran to the Houthis was seized).
I call it minding their business because they are just fighting a proxy war against the Saudis. An enemy that has sought (and still seeks) their destruction. So fair game i guess?
Nope. First of all, Saudi isn't seeking their destruction anymore. When was the last time the threatened Iran with destruction? Secondly, they are fighting Israel in a proxy war and threaten it with destruction on a weekly basis, even though Israel has never sought to destroy Iran. How is Israel their business? They are also meddling with internal Lebanese politics by arming Hezbollah, how is that their business?
Assad is fighting against radical Islamists no?
No and yes. There are many Islamic groups in Syria fighting each other. Some Assad supports, some not. Some Iran supports (Hezbollah), some not. Iran definitively wants to get a foothold in Syria in order to create a new front vs. Israel, and they have attacked Israel from Syria already.
Are you aware of the history between Iran and the US?
Judging by what you wrote, probably more than you.