Can I live in Thailand for a year with a 90-day student visa?

All non formal education visas are 90 days at a time.

It's not a 1 year student visa. Non-ED visa is a 90 day visa. During the last month of your 90 days your school will provide you with paperwork to take to immigration to apply for a 90 day extension. Then you'll repeat this process up to 4 times.

Immigration wants to make sure you're actually attending your classes and that you are making progress in learning, so you have to go and apply for an extension with paperwork from your school, your attendance records, etc.

The only people who can receive a 1 year education extension are those attending university for a degree.