Does each account in an organization have a 30 day free trial for AWS PCA

For AWS Organizations, the AWS Free Tier eligibility for all member accounts begins on the day that the management account is created

Reference : https://docs.aws.amazon.com/awsaccountbilling/latest/aboutv2/billing-free-tier.html

No, Free Tier is one for the whole Organization. As Nitin replied above - all member accounts pretty much "sign up" to the Free Tier plan of the Management Payer account (if Payer is still on Free Tier). It means that, for example, you get only 1 Linux instance and 1 Windows instance for free for 1 year for the whole Organization.

Another example: if the Payer is no longer on Free Tier (or you use up all your limits), and let's say there is a new account that had Free Tier before joining. That account will lose its own Free Tier benefits when joining that Payer.