If my friend register for a free aws account on Dec 30, is the free 12 months plan free until Nov30 or Dec 31 next year?

Hello.

The account is valid for one year from the date of activation.
In other words, if you created an account on December 30th, your free tier will expire next December 30th.
https://aws.amazon.com/free/free-tier-faqs/?nc1=h_ls

Q1: What is the AWS Free Tier?

The AWS Free Tier provides customers the ability to explore and try out AWS services free of charge up to specified limits for each service. The Free Tier is comprised of three different types of offerings, 12 months free, always free, and short term free trials. Services with 12 months free allow customers to use the product for free up to specified limits for one year from the date the account was activated. Services with an Always Free offer allow customers to use the product for free up to specified limits as long as they are an AWS customer. Services with a short term trial are free to use for a specified period of time or up to a one-time limit depending on the service selected. Details on the limits and services provided for free are detailed in each card on the Free Tier page. If your application use exceeds the Free Tier limits, you simply pay standard, pay-as-you-go service rates (see each service page for full pricing details). Restrictions apply; see offer terms for more details.

Q2: When does the AWS Free Tier expire?

Services with 12 months free allow customers to use the product for free up to specified limits for one year from the date the account was activated. Services with an Always Free offer allow you to use the product for free up to specified limits as long as you have a valid AWS account. Services with a short term trial are free to use for a specified period of time or up to a one-time limit depending on the service selected. Additionally, short term trial period may start when you first use the service, not when you create your account. When your Free Tier expires or if your application use exceeds the Free Tier limits, you simply pay standard, pay-as-you-go service rates (see each service page for full pricing details). Restrictions apply; see offer terms for more details.

You can also check the usage status of the free tier by following the steps in the document below.
https://docs.aws.amazon.com/awsaccountbilling/latest/aboutv2/tracking-free-tier-usage.html