Yes, Apple's computer warranties are international. Worst case, you have to ship your product back to the purchasing country if Apple asks for that, but the wording and common practice is U.S. purchases generally get covered everywhere Apple has service globally.
See Apple's Warranty Page for more details. The warranty is established in the country of purchase and if warranty service is not available in the country where the device is when service is requested, you may be on the hook for import/export duties as well as paying for the shipping.
No, iPhone and some parts of AppleCare plus are not necessarily international.
Pay attention to parts like:
IMPORTANT RESTRICTION FOR iPHONE, iPAD AND APPLE TV SERVICE.
Apple may restrict warranty service for iPhone, iPad and Apple TV to the country where Apple or its Authorized Distributors originally sold the device.
That doesn’t mean you won’t get service, but you could be denied or could have to get the device back to the country of purchase on your dime to get service.
Also, no in terms of consumer law varying widely between Europe, Asia, US and other countries:
- Warranty is what Apple offers and you may have responsibilities or costs to get service
- Consumer law covers things outside the warranty, so you need to balance both when choosing where to buy
- Look for words like shall and may and must - these contracts are legal and /or prescriptive so details and words matter. Read all the document, several times before spending money if you don’t know the return policy or have limited time to return goods after purchasing them.