Short answers, pulled from the story.
The Bush administration's primary stated rationale was that Iraq possessed weapons of mass destruction and that Saddam Hussein had ties to al-Qaeda. Both claims were later proven false: no WMD stockpiles were found, and the 9/11 Commission concluded in 2004 there was no credible evidence linking Saddam to al-Qaeda. The Iraq Liberation Act of 1998 had already made regime change official US foreign policy before the September 11 attacks.
The Iraq War began at 5:34 am Baghdad time on the 20th of March 2003, when the United States, joined by the United Kingdom, Australia, and Poland, launched a bombing campaign. US forces were officially withdrawn by the 31st of December 2011 under President Barack Obama, though the United States became re-engaged in Iraq in 2014 following the rise of the Islamic State.
UN Secretary-General Kofi Annan declared on the 16th of September 2004 that the invasion was not in conformity with the UN Charter and was illegal. The 2016 Chilcot Report, a British government inquiry, concluded the war was unnecessary because peaceful alternatives had not been fully explored.
The war led to an estimated 150,000 to over a million deaths, with more than 100,000 of those being civilians. Most deaths occurred not during the invasion phase but during the post-invasion insurgency and sectarian civil war.
Curveball was the codename for Rafid Ahmed Alwan al-Janabi, an Iraqi emigrant living in Germany whose claims about Iraqi weapons programs were used by Secretary of State Colin Powell in his presentation to the UN Security Council on the 5th of February 2003. Both German and British intelligence had warned before the presentation that the source was untrustworthy. Al-Janabi later admitted his claims had been fabricated.
The troop surge was a plan announced by President Bush on the 10th of January 2007, involving an additional 21,500 troops deployed to Iraq under the command of General David Petraeus. The US Defense Department reported overall violence dropped 80 percent by December 2008. However, investigative reporter Bob Woodward cited US government sources who attributed the drop primarily to new covert targeting techniques rather than to the surge itself.