Iraqi shia's were never oppressed the way the kurds were by the Baathist regime or the ones before it. Since you don't any historical background on Iraq and its people, let me tell you the ones that regime did persecute and kill, they all belonged to the Shia political group called Hizb Da'awa the first such kind of Shia group to come by that called for the establishment of a shia "Islamic" state founded by a cleric that belonged to Sadr family and it modeled itself or got inspired by the works of Sayid Qutb and the Muslim Brotherhood and that ideology even went to Iran and inspired Khomeni who laid down the foundation on how a shia state could be established under the absence of the Mahdi because the main reason why Shia Arabs in Iraq or in Lebanon couldn't get active on politics in the country was for them to wait for the reappearance of the Mahdi who will establish his reign and state but the students in the Howzat and young clerics in Najaf wanted their sect to be active and there's no need to wait the Mahdi to apply their version of shari'ah on the land and it was revolutionary idea that moved young shi'as both in Iraq and Iran which led such groups to be classified as a threat to both regime.
Iran during its war with Iraq after it kicked out all Iraq troops from its territories in 1982, Khomeni instead of taking the victory and calling for a ceasefire, he openly declared to topple Saddam's regime and export its revolution throughout the region thus the war took another bloody 6 years without Iran achieving its goal of invading Iraq but it get a lot of support from the Iraqi Shi'as who got inspired with the Islamic shia system Khomeni put in place in Iran and many have declared their allegiance to him and his system.
With that support Iran got from Iraq Shi'as it created for them a political opposition groups and militias who will carry out terrorist acts inside of Iraq and call for the regime downfall by lobbying western states to sanction Iraq.
That group is Supreme Council for the Islamic Revolution in Iraq, (SCIRI), and its leader was Abdul Aziz al-Hakim who was member of the governing council set up by Paul Bremer diring the early days of the occupation and he was a loyal to the waliya al fiqih of Iran who's Khamenei.
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Hezbollah was founded by the IRGC in the 80s with the help of the Syrian regime and its allegiance first and foremost lies to Iran and its supreme leader.
After the end of Israel occupation in Lebanon , the Hezb should have dropped all its weapons and dismantled it armed wing but no it took Lebanon into another disastrous war in 2006 when they abducted 3 Israeli soldiers by infiltrating into Israel and Hassan Nasarallah admitted to the public that if he knew Israel will act the way it did , he wouldn't have approved the abduction of IDF soldiers.
In 2008 Hezb and its allies forcefully took over and occupied Beirut to topple the Lebanese govt that took some drastic measures against them and it only took Qatar intervention to end the hostilities that cold have sparked another civil war but the winner was Hezbollah as it took the state under its hands and since then nothing could have been moved forward without the approval of the Hezb with the latest being the vacant presidential post where Lebanon hasn't had a president for almost 3 years now.
Syrian revolution was people led revolt against the autocratic sectarian
atheist Baathist regime that has been in power for almost 40 years and the regime has responded to the people who demanded a change in the most horrific ways by abducting activist and torturing them in their jails and sending the army to shoot to kill the people who have gathered in squares in the center of the cities so those soldiers who didn't want to carry out those orders, defected and fought against the regime and the regime called help from Iran who send their men and its proxies from Iraq Lebanon Afghanistan and Pakistan to kill and displace Syrians from their homes for being Sunnis as Iran have stated their presence in Syria the land of the Ummayads was a religious duty to avenge the blood of Hussein from Yazid followers aka Syrian people.
Saudi Arabia was the main reason on why the revolt against Ali Abdullah Saleh succeeded where the president stepped down and handed over the power to his vice president this bringing an end to the revolt or uprising.
Houthis on the other hand a launched a sectarian armed struggle rebellion against the state with weapons and experience provided by Iran through its proxy the Hezb in which they violently took the capital Sana'a 10 years ago which ignited the civil war and Yes Ali Abdullah Saleh shares the blame for that group being power as he thought through them he can get back to rule Yemen again but he underestimated the group's power and how they subjugated most of the tribes through bringing back the Imamah zaydi style of governing in the society so the Republicanism spirit in that has become the identity of his home city during 26th of September revolution in 1962 was gone and it was already too late when he found out about it and he got himself killed at the hands of the Houthis whom he helped to take over the state.
Syria Yemen and Lebanon.