There will be a few issues. Sort them before you buy. It could be too late after you buy.
What is the tax treaty between the USA and Norway? How will things like depreciation be handled? If you depreciate in the USA and the Norwegian tax system does not recognise it as a valid deduction, you could be paying tax in your home country. I know from personal experience given the USA and UK tax code does not line up on this specific topic.
Second, you might want an C-corp rather than a pass through entity (S-corp or LLC). Similar logic. Where does the income and capital gains land.
Third, you need to think about credit and what your long term strategy is all about. Are you likely to move? If not, what about the currency exposure? If you are going to want to bring the gains back to Krona, you need to think about how much the FX rate will move around. If the property appreciates by 10% yet the FX rate shows the Dollar weakening, you could still be looking at a paper loss. Real estate is a bad way to speculate on a currency. Better to take a long term view and reduce the frequency you might need to move funds one way or the other. Can you operate a bank account in your home country which allows you to hold USD? If so, you can reduce the frequency of FX transfers even when you choose to bring the funds home. Or, operate a USD account in the USA and leave the funds in the USA.
After you have your strategy for how you will hold the assets, then you can worry about which registrations you need to sort for yourself personally vs the business entity you are using.
AML is not hard to deal with if the funds are easy to verify. Just expect delays when you first move funds to the USA. Definitely consider moving the funds long before you need them.