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A foreigner can buy a car in Serbia without issues. Like anywhere else in the world, as long as you buy from a reputable dealer then you shouldn't have any problems. The important thing to remember as with anything in life is that if the deal sounds to good to be true then it most likely is and you should avoid it unless you are prepared to gamble and risk losing.
For a loan, once again, yes you can obtain credit PROVIDING you have some form of residency visa. If you have a temporary residency visa then your loan agreement will only last for as long as your visa does so, if you have a brand new temporary residency visa that is valid for 12 months then you could find a loan agreement but it will also last only for 12 months so your monthly repayments might be quite high.

Hi, I was wondering if it's possible to buy and register a car in my name as a tourist. I'm not living, nor registered in Serbia right now (looking to move if I like the country)

I will buy a used car for a long vacation in Serbia.

Is there a website to figure out taxes and car insurance?

Kind regards

@Isapft I don't think it's possible if you don't have at least a temporary resident permit.  Unlike the American system, where a visa is all you need to stay in the country as a foreigner, the European system uses a visa only for entering the country and a short stay. If you want to stay for more than 3 months, you must pursue either a temporary or permanent residency before your 3 months run out. After all, a tourist can only stay up to 90 days. Do you really need to own a car for just 3 months? This is Europe. Public transportation is very convenient. I left California in 2021 and bounced around Europe from country to country as a nomad. I have NOT had the need to drive! If a Californian can go for nearly 2 years without a car, anyone else can do it. If you really want to visit a place that is not serviced by public transportation, rent a car just for that trip or hire a taxi. It would be much cheaper than owning a car. Parking is often a headache in a European city. Fuel is absorbently expensive. Add tax and insurance to it, you would want to avoid car ownership as a visitor.

Though not part of your question, Belgrade, Serbia is no longer a good place for your money. The influx of privileged Russian kids who come to Serbia to avoid military conscription back home has driven the rent up like 3x since 2022! Because of Serbia's refusal to participate in sanctions against Russia, Serbia becomes an obvious escape for them. However, just because the rent went up 3x (yes, it's war profiteering), it doesn't mean the standard of living has increased at all! You have to ask yourself why you are paying almost the same price as Budapest, Hungary, but the latter has much better infrastructure, not to mention the grandeur of an old empire. Certainly, you can live in the Serbian countryside and pay less, but what can an expat do there anyway?

I only come to Serbia because it's close to Hungary. With a U.S. passport, I can only stay visa-free in the EU for 3 months every 6 months. So I reset my clock by coming to Serbia.  By the way, though Serbia is not a member of the European Union*, a visa-free stay is also 3 months.  When my time is up in Serbia, I go back to the EU.  Certainly, Serbia isn't the only place where one can reset his EU clock.  I choose to come here because it's a short car ride from Hungary.  When the high-speed train opens in 2024, it would be even more convenient between Budapest and Belgrade.  (*I am using the EU and Schengen zone interchangeably because many people outside of Europe don't know what Schengen is.  The 2 overlap to a large extent but not exactly.  For example, Bulgaria is a member of the EU but not in Schengen.  So you can reset your Schengen clock by going to Bulgaria too if the country is your cup of tea.)

@Isapft

"hire a taxi" <= certainly, you go as far as you can on public transportation first and use a taxi only for the last leg.

@Isapft

If a foreigner in Serbia has been granted temporary (at least 6 months) or permanent residence, he can purchase a car and register it in his name.

A tourist who does not meet this requirement cannot register a car in his name in Serbia, but he can purchase one.

A car can be rented for a reasonable price from one of Serbia's many car rental agencies.