When and why are catechism used? Are they typically said every Sunday?
Catechisms are normally used to instruct youth who are about to be confirmed, or an adult preparing to enter the church from a different tradition. The process goes back to the early church, where special instructions were given to converts before they were baptized.
How they are used is up to the person who is responsible for the preparation. At least in the PCUSA, the pastor normally is responsible for preparing candidates. It's common to have a weekly class. Whether it uses a catechism or not is up to the pastor.
You could certainly use a catechism at home or elsewhere either to instruct a child or to learn more about the faith yourself. If so, the frequency would be up to you, but if it's much less than weekly it might be hard to maintain continuity.
While the classic catechisms are great documents, I wouldn't recommend using a catechism alone either to instruct someone else or learn for yourself. I'd use a good book about Presbyterian theology either with the catechism or in place of it. Specific recommendations would depend upon your theological orientation and the age and maturity of the candidate.
The traditional Presbyterian catechism is Westminster. It's going to be a few years before you twins would get anything out of it, but you might yourself. However I'd suggest for you something more like "Presbyterian Beliefs: A Brief Introduction" by McKim. Or for a more conservative equivalent (though I haven't read it): "On Being Presbyterian: Our Beliefs, Practices, and Stories" Sean Michael Lucas. (Another possibility is "What is Reformed Theology?: Understanding the Basics" by R. C. Sproul. However it seems to concentrate on a few beliefs that separate Reformed theology from others, where I'd prefer a treatment that deals with all the basics from a Reformed point of view.) I'd probably read an introduction like that before trying to tackle Westminster.
What is being confirmed? I will look up the things you mentioned. Thank you very much