Does Apple have currency conversion fees?

No. See the following from https://www.goldmansachs.com/terms-and-conditions/Apple-Card-Customer-Agreement.pdf

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.