There is no charge for a free trial. Users get charged for staying subscribed after the trial period. For the 4th month and later.
The default billing period is monthly, but users can change it to annual for a bit of a discount. Once per 3 months is not an option for this.
Not everyone may qualify for a free trial. The extended free trials are in combination with buying an eligible product or service. What is your qualifying product or service?
For most offers, users have to redeem on their new qualifying product, else the offer may not get applied.
There will be a time limit after which the offer is no longer valid to be redeemed.
Possibly something was ordered that is not part of Apple TV+. Other streaming content or streaming services will be charged separately. E.g. Max Ad Free is 15.99/m. Some buy or rent movies may be 15.99.