I suppose it comes down the literal meaning of the words "United States" at the time of the Revolution. The colonies acted independently, sending representatives to a Continental Congress that had more in common, powers-wise, with the modern United Nations than the Congress of the United States. The Continental Congress was originally a place to discuss coordinating protests against Parliamentary overreach; it only gradually and unevenly took on the trapping of a national government. As such, the several, separate states united together to form a government, rather than the central government dividing its territory into provinces. Think bottom-up, instead of top-down.

I can't comment on the reason behind the existence of US states but I can comment on the second question.

Australia is also largely comprised of independently governed states in a similar way that the US is (Australia also possesses a number of federal territories). Before federation, Australia was made up of individual, self-governing colonies. The road to federation is rather long and not necessarily interesting unless you have an interest in political history.

What is interesting is that during the road to federation a number of examples of other countries achieving federation were looked at. At the 1890 convention, delegates considered the example of the Canadian constitution but found it to be too centralised, many of the smaller Australian colonies were intent on retaining a large amount of their autonomy and feared being dominated by the larger colonies of Victoria and New South Wales. As a result, delegates inevitable turned to the example of the US constitution and the example it set of the protection of state's rights. Suggestions were also made to model the style of government on the example set by the US. There has been quite a bit of literature written on the similarities between the Australian Constitution and that of the US. I would speculate that, in regards to your first question, the existence of states in the US originated from a similar desire to retain a certain level of autonomy and rights.

Sources: The Americanness of the Australian Constitution by Patrick Keyzer

The United States didn't really decide it. Britain did. The British Empire considered the U.S. to be the 'Thirteen Colonies' because there really were thirteen of them. As such, when each seceded, they were technically thirteen independent states, which then confederated into what we know as the USA with the famous Declaration of Independence.

It is very rare for a nation to come about in such a way. India, for example, is separated into states, but that's something I know much less about.

As for following that example... well, it didn't work out so well for the States themselves. They tried to retain massive local autonomy and still be a unified country using a proto-Constitution called the Articles of Confederation. You can read the document directly from any number of online sources (here's one) and it lays out some surprising ground rules, such as a free opt-in for Canada.

However, you'll recognize that almost all actions that this U.S. Congress has to carry out as a government of a sovereign state must be approved by nine of the then-thirteen states.

The United States in Congress assembled shall never engage in a war, nor grant letters of marque or reprisal in time of peace, nor enter into any treaties or alliances, nor coin money, nor regulate the value thereof, nor ascertain the sums and expenses necessary for the defense and welfare of the United States, or any of them, nor emit bills, nor borrow money on the credit of the United States, nor appropriate money, nor agree upon the number of vessels of war, to be built or purchased, or the number of land or sea forces to be raised, nor appoint a commander in chief of the army or navy, unless nine States assent to the same:

There are various other issues with the document, including the phrases "each state retains its sovereignty, freedom, and independence" and "firm league of friendship" which raise some eyebrows, and eventually people realized that this wasn't the way to run a country.

The Constitution would be ratified about six years after the Articles were. In that sense, the American experiment with statehood was a failure. Even today, there are issues with states having the autonomy they have. Debates over states' rights are still a thing.

It's pretty fun to look through the Articles (it's a short read) and see what issues you yourself can point out with the document. That's something I had to do in high school. You can also look up The Great Debate for some further reading. This was a real debate between two U.S. Congressmen over states' rights in the early 1800s. It's a primary source and both sides bring up some great points.