1) Was there any serious discussion of taking the US to the international court for war crimes?

No for reasons of context.

Bear in mind that there was very little international criminal law at the time for them to break. While it was probably possible to construct a legal argument for why the US as a whole had violated the laws of war (excessive collateral damage; "terrorism" in the original sense of the word, i.e., states trying to terrorise civilians), there was no mechanism for deciding which US citizens were responsible and should be tried for such crimes. There was no "international court" at the time that had a shadow of a claim to such a powerful jurisdiction.

The Nuremberg trials were built entirely from scratch and they define the field of international criminal law. They chose who appeared before them and it was a very limited number of very high ranking Germans. The US was instrumental in building it (they did a fair share of the logistics and they loaned their Chief Justice of the SCOTUS to run the thing) so they didn't really need to fear it. If the court had decided to threaten them, they could have just pulled the plug on its finances. The victors chose the judges!

Even today, it wouldn't happen as you describe it: the US as a country can only be hauled before a court if they've broken a treaty, if they're willing to or if they're accused of something they have given a waiver for (genocide for example). War crimes are the purvey of individuals, not countries.

2) Was Nuremburg a victor's justice?

It's complicated. People at the time debated this exact point and there are records of US judges arguing this exact point with each other. It's worth noting that the proposed alternative to a trial was "put them up against a wall and shoot them", i.e. recognise that they were being killed because they were the losers of a war.

I'm of the opinion that it isn't fair to call it victor's justice. Yes, it was literally justices of the victors judging and condemning the losers; yes, the Allies also committed war crimes by the metrics used at Nuremburg and yet escaped trial; yes, the trial had a mostly political and PR purpose. However, it is undeniable that the tribunals limited themselves to a far smaller set of individuals than it needed to and they went to pains to offer the accused as great an ability to defend themselves as possible and was extremely fair in taking their individual circumstances into account. In many ways, it was like international prosecution today: very fair to those it does capture, only punishing people who have in fact committed heinous crimes but very selective in who it is able to indict and capture.

3)Did the US suffer any immediate blowback from jurists and legal scholars after the bombing of Hiroshima and Nagasaki?

Yes, very much so. The reaction to the bombings was pretty intense: a stunned horror mostly. Camus wrote that it was the moment our civilization was confronted with its mortality.

Truman went to great pains to stop people realising just how bad it was and explicitly covered up the elements that made this a war crime. He quickly made public speeches in which he stated that they hadn't bombed a civilian city but a military-naval installation; a lie, but a necessary one if he wanted to prevent legal blowback. His administration very quickly started to lie about the amount of radiation it gave out when reports of people falling sick days after the bombing started to make the news. The rationale here was a realisation that legal scholars were looking over the conventions against chemical warfare and drawing analogies between radiation and poison (a lingering effect that kills people, they're functionally very close).

We even have reports written by the military in which they made the case why the use of this weapon was perfectly within the parameters of the laws of war and was simply a weapon like any other. From that, it appears that they just didn't realise how fundamentally different nukes were. As far as they were concerned, this wasn't causing significantly more deaths than the Tokyo fire-bombings and they had paid billions to build this thing so they were bloody well going to use it. They didn't perceive it other than a purely military one and so were caught by surprise when Truman got angry for the second use. This was just a new toy in the arsenal, a purely military matter, why the hell did the president expect them to ask for permission every time they used one? (Truman found out about Nagasaki in the news like everybody else, he wasn't pleased).

tl;dr

The US never risked any legal consequences for their crimes but they didn't want to be perceived as committing war crimes; when the bombs dropped, they went into PR overdrive to sweep uncomfortable facts under the carpet and believed themselves that they had in fact committed war crimes.

Apologies for the lack of citations, this is mostly from memory of my IL classes and textbooks which I no longer own.

u/restricteddata has written extensively on the bombings. One of the biggest pushbacks was from Americans themselves. The Nagasaki bombing happened the same day that the first damage assessment reports from Hiroshima reached Washington. And Truman ordered that there would be no more attacks without his permission.

What law, specifically (paragraph and line) was being broken to attract the attention of jurists?

It is important to remember the distinction between something which is morally questionable, and something which is legally questionable. It is also important to remember that the laws of war have changed over the last few decades.

The bottom line is that aerial bombardment of cities was not a considered war crime. Dropping bombs on London, Dresden, Coventry, Koln, Tokyo or Nagasaki was simply part of total war, and, aerial bombardment of cities was one of the strongest arguments put forward for the creation of air forces in post Great War thinking by the early theorists such as Douhet, the Italian aviator. These new airplanes of greater bombing capacity could avoid the repeat of the horrors of the Great War by simply flying across the line and attacking the enemy’s vital centers, thus destroying their morale and ending the war with much less bloodshed. Translation of his 1921 paper here. https://permanent.access.gpo.gov/airforcehistory/www.airforcehistory.hq.af.mil/Publications/fulltext/command_of_the_air.pdf

Douhet was highly influential worldwide. Obviously nobody is going to go about officially proposing in accepted documentation that one commits war crimes as a matter of course. The current Geneva Conventions were drawn up in 1949 to reflect the latest thought resulting from WW2. One of those observations was that the strategic bombing campaigns, particularly the firebombing such as of Dresden or Tokyo, should be outlawed.

Note how almost nobody (One exception) on either side was tried for war crimes as a result of a bombing campaign on a city. There are two arguments for this. One is the equivalency argument: Legal or not, both sides did it, and they could not convict someone for acts carried out by their own side: A notable example was Doenitz’s acquittal on the charges relating to submarine warfare: US officers testified they did the same thing. In the case of air bombardment, I don’t believe any charges were even brought in the first place. If such is the case, then the argument for "victor’s justice" fails. The other possible reading of the situation was a purely legal one: Bombardment of undefended civilians was a war crime, but most cities were not undefended or unrelated to other military purposes. London was defended by anti-aircraft artillery and fighters. Thus, it was a legitimate military target for the Germans, and there was no call to come up with a war crimes charge for the action. The one exception I mentioned is the case of Belgrade, the Yugoslavs had explicitly announced Belgrade to be an undefended open city, and the Germans bombed it anyway. This was considered to be a war crime, for which General Alexander Loehr was convicted and executed. Perhaps it was a ‘loose’ interpretation of defended areas which was deliberately chosen in order to allow the bombing, but it was a legitimate one regardless.

Thus not only was the aerial bombing of cities generally considered an acceptable way of doing things by air power theory in the 1940s however brutal it may have been, there is no demonstrated different application of the rules from the Allies to the Axis.

This leaves only open to question the nature of the weapon itself as a source of criminality. Of course, as a new invention, there was nothing in the law outlawing them, and in terms of pure deadliness, the Tokyo firebombings killed more people than an A-bomb drop, so the overall effect was less. The A-bomb was a particularly devastating and effective bomb, but just a bomb nonetheless.

Post war changes in the laws have both specifically prohibited aerial bombardment of cities with incendiary munitions and added additional requirements on proportionality. As a result, today there would be no question that Tokyo bombing would be a war crime, and it would be extremely likely that Nagasaki and Hiroshima would be. Such was not the case in 1945, so there would be little grounds for a jurist to claim legal issues with the bombings, even if there were a motivation to do so.