Is it possible for Americans to get jobs in other countries...like Italy? Or Sydney, Australia?

yes if you haver a work visa

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Yes, but it can be complicated.
If you have a specialized/desired skill such as medical/computer it is easier.
If you already have a job and thus a sponsor it is easier.
There are some firms which will place you in a country and even pay your way there. You become, essentially, an indentured servant. Many of the European immigrants early on came this way. A significant portion of your pay check then goes to the company to pay for their cost.
When you have a job, you can only work for so long w/o your employer saying you are necessary and similar work cannot be done by native born.
My son has done each of these in China. After 7 years, he will receive a permanent D visa which allows him to come and go from the country.
Asian nations are especially interested in Americans. My son "pronounces" English. The native population teaches English, but they want Americans to pronounce it.
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