It's common knowledge that the Austro-Hungarian Empire consisted of a relatively large amount of different ethnic groups, and that the Empire was broken up following its defeat in World War I. However, a lot of thought must have gone into how it should be broken up, who would rule which territories, etc., and this must have been quite a monumental task to perform efficiently and peacefully.
Woodrow Wilson had his Fourteen Points, which stated that the people of Austria-Hungary should be accorded "the freest opportunity to autonomous development". This resulted in new nations including Czechoslovakia, Yugoslavia, and an Austrian Republic. But there was also a Hungarian Kingdom, and some lands were ceded to Poland and Italy.
How was it decided that, say, Czechs and Slovaks should share a country? Or that Slovenes should be part of a larger union in the Balkans, and not have their own country? Why was Hungary allowed to have a monarchy, but Austria and Czechoslovakia became republics? Who made these decisions and how? Was there conflict and disagreement among the various ethnic groups of the Empire during this time?
Just a short answer to a complex question: The breakup wasn't performed efficiently and peacefully. The new borders were more or less those of the medieval kingdoms and counties that have been incorporated in the Habsburg empire, leaving behind states that shared the same problem as the former empire: ethnic minorities, that didn't feel represented by the state they lived in. The decisions were note made by the people but by the peace conferences in Paris.
South Tirol although nearly homogenous German speaking was annexed by Italy. It was subject to enforced Italianization like Trieste with a strong Slovenian minority. Heavy fighting took place in Carinthia between SHS-troops and local militia. Therefore, an Allied commission supervised a referendum about the future of Southern Carinthia. Although mainly populated by Slovenian peasants Southern Carinthia voted to remain in Austria. Smaller skirmishes happened in Western Hungary also followed by a referendum deciding the fate of the capital Oedenburg/Sopron that remained in Hungary while the rest joined Austria.
To decision to build a common state with the Czechs wasn't made by the Slovakian people but by some politicians in the capital Bratislava. The parts of Moravia and Bohemia with a German majority wanted to join Austria or Germany but that was prohibited by the Allied powers and by the Czech government. Therefore German represtantives didn't join the national assembly that established the framework of the new republic.
Galicia and Bukovina were inhabited by Poles, Jews, and Ukrainians. The Ukrainians wanted to join the newly established Ukrainian state. On the other hand, the Poles wanted to prevent an Ukraine controlled by Russia and conquered large parts of the Ukraine leading to the Polish-Soviet war.
In Hungary the communists seized power. They refused to accept the new borders and went to war with Czechoslovakia and Rumania. The Hungarian Red Army conquered Slovakia but was defeated by the Rumanian army that seized Budapest and overthrew the communist government. Although the former King Karl of Habsburg tried twice to stage a coup to regain power the former Admiral Horthy established himself as regent leading to the saying: Hungary is a kingdom without a king ruled by an Admiral without a fleet.
I hope that gives you an insight in the complexity of the problems all the parts of the former Habsburg empire had to face after the breakup. To answer all your questions in depth would need some days.