Hello, my knowledge is three kingdoms with some of the Latter Han. I hope this is useful in providing some idea of at least some part of the period you are looking at. Just to note, not all of them had Chancellors, Wu and Shu did but Han and Wei didn't.

The Son of Heaven's position depended on the situation at the time. Several were under regencies or a controller (some killed, some abdicated, some managing to free themselves) where they had no real say whatever so ever at one point or another. That the General in Chief (or a military controller of various high rank) or Empress Dowager ran the country and the Emperor was a puppet, could not make policy decisions. Well till the Emperor tried to gain power or was a bit too open in objections...

However, your question seems to be about when an Emperor was of age and in power. What an Emperor said would, if push came to shove, usually be followed (not always, some Han officers like Wang Yun would breach amnesty), after all, he was the Son of Heaven. Even those inclined to delegation like Liu Shan of Shu or Cao Rui of Wei shaped their era via their personality and authority.

However, any Emperor would hopefully be aware of the power balances in his kingdom. The Son of Heaven may need to be obeyed but that didn't stop the Han slowly being strangled by an inefficient tax system that left it in a finical spiral as unable to use the resources of the Empire, dealing with problems of vendettas, students protests and refusal to serve out of protest. Or Wu, the power balance leaving the Sun clan starved of resources and real power with troops and resources in the hands of the powerful gentry clans. How an Emperor dealt with those powerful clans (getting them on the side, building rival factions like the eunuchs, attempting to reassert authority by force and in some of Emperor Ling's actions, trolling) would be important in shaping their reign and shape their reputation.

An Emperor could try to push through something on his own but often, needing to gather advice, keep people onside (your ministers might not be too happy to be left out of the loop) and to carry it out (your generals for a war), there would be debates and discussions. This would range from big decisions like going to war, infrastructure spending to private matters like the size of the harem and who should be Empress (or the heir). As well as one's chosen counsel, others would soon send in memorials on the matters to make themselves heard, again ranging from punishments and rewards to how often an Emperor was visiting his harem (or how little). The tone could range from respectful, discreet plea to firm rebuke or even the insulting.

The Emperor, if the plan divided court or was opposed, would have to decide how much he was willing to push through. Could he, in practice, implement it without the support? At what cost to political capital would pushing through this idea mean? Would it be better to cede on this and save one's authority for other means? There were other reasons to refuse, the idea simply may be exposed at not the right one after discussion, it could be a personal dynamic that leads an Emperor to hold off out of respect or being overawed, other events occurring meaning idea is shelved.

Could the bureaucracy override an Emperor (aside from controllers)? Refusals did happen, modestly refusing an honour (or making a show of refusing it), fleeing into exile to avoid arrest (often with help), refusing to serve (or in Wu scholar Zhang Zhao's case, refusing open his front gate after a row with his lord Sun Quan, his Emperor promptly set the gate on fire), of wine at a banquet. Issues of personal rather than the state.

Outright blocking a policy, I can't think of one happening during latter Han and three kingdoms. An officer could use his personal authority and dynamics to object, use his allies to build an alliance against it to put pressure on the Emperor, protest via a memorial, cite texts and omens as to why this idea would be bad, even resign, to try to put pressure on the Emperor against it.

How much say would the chief ministers have, it depended on the minister and the Emperor. Some were in honorary positions, some were to appeal to a segment of the bureaucracy without the Emperor really backing them, some would be a political signal. Some would use the positions of high authority with energy and skill, others impact is not recorded. Others in lower position but that were still important (not entirely unknown for figures to take a demotion to take such roles that might be deemed important) or had the Emperor's ear might have more influence. Repeated rejections of the chief ministers and failure to listen however were unlikely to go down well.

On the flood question: People would use that as bad omens to critique the government, the Excellency of Works might well be dismissed, the Emperor offer sacrifices if bad enough and seek advice as to what the omens meant. A relief effort for the local area might well be made following usual patterns of tax relief, resettlement, loans, use of public granaries or land with sometimes officials sent from the capital to oversee it. The officials in the bureaucracy could handle most of this unless the Emperor wished to make a public showing by cutting back his expenses, investigating the prisons, sacrifices or whatever might be required to appease the heavens.

Sources:

ZZTJ by Sima Guang, translated by Achilles Fang

SGZ by Chen Shou, translated by Yang Zhengyuan

Fire over Luoyang and Generals of South by Rafe De Crespigny