How does warranty on a MacBook Air work if I buy in the US and take it to the EU?

1. Like to buy a MacBook Air in the US , I live in Europe.

You would have to travel there, as Apple doesn’t ship internationally. Import duties would apply on the trip back, probably driving up the cost beyond the basic price difference (that is the main reason for the tariff!). Also note that listed US prices do not include sales tax yet, but you’ll have to pay that extra percentage to the shop.

How is the warranty handled ? In Europe we get a 2 year warranty period

The terms and conditions of the country where you buy the product would apply, so: 1 year limited warranty.

EU/national regulations only apply to products bought in the EU or the home country.

2. Can I buy Apple Care in the US and is it valid in Europe ?

3. How about repairs, can I bring it to a Apple store or certified repair shop?

These two questions are basically the same, as AppleCare+ is mostly about hardware issues (repairs).

AppleCare+ should be purchased in the same country as the product.

AppleCare+ for Macs has global repair coverage¹ — unlike for most other Apple devices.

Apple Authorized Service Providers are independent businesses, and may have their own prices and conditions. They may do certain repairs for free or reduced cost, if that repair falls under an agreement with Apple to compensate them for it. Get an estimate before dropping off your Mac there, as it may differ from interacting with Apple directly.

You are asking other end users here, not Apple. We cannot give official answers, especially on legal issues, so this is a bit beyond the scope of these mutual tech help forums populated with people who do not work for Apple..

All warranty documents are here:

Legal - Hardware Warranties - Apple

Select your device and country to see what has been published. As several of the terms are affected by local consumer laws, please see the versions posted for your country.

You need to talk to Apple for further details, exceptions, or questions, but they will not see your question here. They have a EU corporate presence in Ireland:

Hmm, vague, as that very same PDF lists examples of service in other countries:

• Service will be limited to the options available in the country where you request service.
• If service is not available for the Covered Equipment in a country that is not the country of purchase, you may be responsible for shipping and handling charges to facilitate service to a country where service is available.
• If you seek service in a country that is not the country of purchase, you must comply with all applicable import and export laws and regulations and be responsible for all custom duties, V.A.T. and other associated taxes and charges.
• For international service, Apple may repair or exchange products and parts with comparable products and parts that comply with local standards.
• Apple may use Covered Devices or replacement parts for service that are sourced from a country that is different from the country from which the Covered Device or original parts were sourced.
• Please note that if you seek service under this Plan in a country other than your country of purchase, the service fee will need to be paid in that country’s currency and at that country’s applicable rate.

AppleCare+ for Macs has global repair coverage¹ — unlike for most other Apple devices.

The defining AppleCare+ document for U.S.-bought Macs includes the "may restrict to county of purchase" language:

https://www.apple.com/legal/sales-support/applecare/applecareplus/2209/220907_applecareplusmac_us.pdf

dated Sept 2022