The contract would be made with the vendor, and would be legally made in the country the vendor is registered in. If you use a credit card, any protections afforded will be in the terms and conditions of *your* credit card, regardless of where the purchase is made. Protection may be less by debit card and will be less by other methods.
As an example. If I commit to purchase some film from my laptop in the UK with my UK credit card, with a company in Germany and another in the USA....both are covered by my UK credit card T&Cs which are pretty compehensive. In a case whre goods hadn't arrived after months I could claim every penny back quite easily and the card company would go after the vendor.
My contracts would be in Germany and the USA, and each would be bound by the laws in those countries and states within the USA.
Either way, first port of call is with the vendor, and if that draws a blank then with the card issuer. Finally with the courts, though you may find your card issuer does this part on your behalf.
It seems a very strange situation going on and I'd be getting worried too.