Predictably, Donald Trump did not consult with Congress about an operation on this scale, nor did he consult with US allies, who have troops and personnel in the region. Unprecedented, but not unexpected, given Trump's past failure to follow precedent in foreign policy matters.
Suleimani was not a good guy by any stretch of the imagination, but killing him was almost certain to be considered an act of war by Iran. So retaliation is certain, but possibly not immediately. I don't think that Iran thought Trump would do something this blatantly provocative, so they will take their time to consider how to response. Right now, those experts on the region that I've seen consulted seem to think that the retaliation will come from Iranian proxies, rather than a direct attack, but it will be obvious that it is retaliation for this assassination. Suleimani was not only an extremely well-known figure in Iran, but also a popular figure. So one immediate effect is that the anti-government protests that have been going on in Iran will end and people will rally around the government there. Over the long term, it is hard to see how escalation to full-scale conflict can be avoided, as each side seeks to save face through revenge and retaliation.
The government of Iraq is in an extremely weak position, and that is why they essentially turned their backs and allowed the US embassy to be attacked briefly. Suleimani was thought to have been one of the strategists behind those attacks, and his name was prominently displayed in graffiti left on walls around the embassy. It is quite possible that Iraq will now feel compelled to expel the US. The most likely response is initially is that US facilities and individuals will be targeted for terrorist reprisals. Iran has a lot of options for responding to this kind of provocation, but an all-out war will likely result in the bottling up of oil exports out of the Gulf.