Are there fees to use the new Apple Cash pay

There are no fees for sending and receiving Apple Cash.

See: Send and receive money with Apple Pay - Apple Support

However, if you use the instant transfer option to transfer Apple Cash to a debit card there is a fee. There is no fee to transfer it to a bank account. That can take 1 to 3 days.

See the following from Transfer money in Apple Cash to your bank account or Visa debit card - Apple Support

A 1 percent fee (with a minimum fee of $0.25 and a maximum fee of $10) is deducted from the amount of each Instant Transfer.