The liberal conservative dichotomy outside of the US
It is conventional practice for Americans to categorise political ideology into two distinct camps of liberal and conservative with no third alternative or middle ground between the two as it is a dichotomy rather than a continuous spectrum. The American definitions of liberal and conservative are different from the British definitions of liberal and conservative, and also, the (loosely defined) definitions of left and right.
Are there any other countries in the world that use a similar liberal conservative dichotomy to that used in the US or is it unique to just one nation?
Not as far as I know. It can't be brought to Australia because the right wing party is called the Liberal party.
The U.S political vocabulary being different helps to prevent American's from getting meaningful insight into issues via foreign media, and keeps people locked into the domestic MSM's framing of issues.
It isn't only the definitions. It's the concept of having just two distinct camps for the whole of society. Especially a society is that otherwise very diverse and increasingly so as each year passes.
There are other nations that have a strong dichotomy but different from that in the US. Northern Ireland being one example with nearly 99% of the population identifying themselves as Unionists or Republicans and the remaining 1% having a difficult time in such an environment. Ulster folk are very well aware that their province is very peculiar in the world, so trying to apply the Unionist Republican dichotomy to other nations is unrealistic and meaningless that it's a false dichotomy outside of Northern Ireland.
The US Liberal Conservative dichotomy is completly alien to my way of thinking which results in difficulties entering into any debates built on a platform of either or both factions on WP or elsewhere.
In the American news sources yes - and probably in order to appease the American palate. In reality the political situation is quite sophisticated and complex.
They have other parties as well with varying degrees of support which makes a dichotomy very unrepresentative. Even in 1950s Britain which was the closest example to a two party system since 1900 the accepted view was a continuous left right spectrum with a strong concept of middle of the road politically rather than a dichotomy or trichotomy clearly mapped onto the Labour, Conservative, and Liberal parties.
One country that is clearly divided into two camps is Spain. If you disregard the complications posed by potentially separatist regions esp. Catalonia, I could categorize most Spanish people I've met as clearly either left or right. The divisions that existed during the Civil War are still alive. The difference from the US is the left is more unapologetically Marxist and the right benefits from a strongly homogeneous Catholic population plus the history of having risen up and expelled the Moors in 500+ years ago, whereas the right in the US has to appeal to an ethnically and religiously diverse audience.
Another but different example is Venezuela.