does apple card work at hotels and overseas

The Apple Card is a Mastercard credit card and can be used where Mastercard is accepted.

You can use it via Apple Pay on a device or you can use the physical titanium card. See: Request and activate a titanium Apple Card - Apple Support

It can be used internationally. Also see the Customer Agreement https://www.goldmansachs.com/terms-and-conditions/Apple-Card-Customer-Agreement.pdf including the following:

TRANSACTIONS MADE IN FOREIGN CURRENCIES

Transactions, returns and credits made in a currency other than U.S. dollars will be converted into U.S. dollars. We do not add any foreign exchange rate fee to these Transactions. The conversion will be performed by Mastercard International, the payment network associated with your Account (the "Network"). The Network follows its own methods for conversions that are subject to change. The conversion will occur on the day the Transaction, return or credit is processed by the Network, which may be different than the date of the Transaction, return or credit. As a result, the conversion rate may differ from the rate as of a Transaction date or the date a Transaction is posted on your Account.