Since you are US citizen, no other tax authorities than IRS can collect your income taxes. Only exception is i) when you have a dual citizenship(US & a country of Schengen area) or valid residence permit of a country of Schengen area(for instance) or ii) when you work and generate substantial income in Italy legally(it requires work permit or visa) or illegally while you are there as a tourist.
However, there’s one huge downside to sending invoices from different countries and receiving payment in different currencies: the fees that eat into your profits.
So how can you stop paying a ton of fees for international payments?
The best payment methods for overseas transactions
When you’re being paid online for international services, you have to understand that you’re going to pay extra fees, in comparison to working with a local client. With that being said, there are still ways to keep more of your hard-earned money.
PayPal
If you’re in the U.S. and being paid through an online service like PayPal, you’re likely to pay 3-4% of the total transaction. If you live outside the U.S. the fees vary according to your country, with a fee of 0.5-4% based on the type of payment method used. Invoices paid with a bank account or PayPal balance have a much smaller fee, versus payments made with credit or debit cards.
If you're unsure, be sure to consult your local tax authorities.
The first step to claiming a freelancer's tax deductions is to officially establish your business. This usually involves registering your business name with local authorities -- depending on where you live, this might mean your state, city, county, and/or province. (Beyond tax reasons, this will protect you from someone else trying to start a local business using the same name.)
Check with your secretary of state or department of labor for information on how to sign up your business. States are getting pretty helpful with this, and for the most part you should be able to do everything online.
When you are registering, it's worth taking the time to think about what business structure you want to use. Most one-person businesses register as sole proprietors, in part because it is the easiest and cheapest business type to register. But know that as a sole proprietor, your personal assets are vulnerable if you're sued by a client or subcontractor in your business.
In the future, you can do re-registering as an LLC, or Limited Liability Corporation. Reforms have made it possible for one-person businesses to use this form of incorporation, which shields your personal assets from business lawsuits.
or you could join other type of company structure (mostly 5-10 small team) and they could be helpful as you just started your career.
I suggest you to register as a sole proprietary.
Finally, is it possible that I don't register a company and don't get any permit and just pay the tax for my income from the freelance tasks?
You can. just politely ask your clients if you may pay the tax for the income. I have done it, but it depends on the client. If the client wants to be official, you may not.
Generally when you are working remotely and the company is in a different country than you are, from a legal standpoint, you are not an employee, but you provide your services as an entity and you provide invoices to the company and get paid. The legal way to provide invoices is to have a company. Depending on where you live, it should be easy to build and register a sole-proprietorship.
Keep all the income and expenses in an excel file and you won't need an accountant in the beginning. Just get the wheel rolling, after that, you hire an accountant for about 10-20$.
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Tip
The best currency for your invoices
The best currency to invoice your clients in is the one you discussed with them prior to starting work.
That being said, the most widely accepted currency is U.S. dollars. Most, if not all businesses use U.S. dollars for international transactions, so it’s best to stick with invoicing clients in this currency.
Disclaimer
You should always seek independent financial advice and thoroughly
read terms and conditions relating to any insurance, tax, legal, or
financial issue, service, or product. I answered as a guide only.