As far as the one week trial for the WWE Network goes, you will still be required to sign up with a credit card at launch. Much like other companies, such as Netflix, the subscription will then automatically renew until you cancel the account.
Speaking of the WWE Network, there has been talk within WWE recently about the idea of doing a cliffhanger-type ending to the February 24th RAW (the night the Network launches) to encourage fans to immediately sign up for the WWE Network as soon as it becomes available.
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(Credit: Wrestling Observer Newsletter)