Does every denomination / sect have a catechism? In Lutheranism, there's the Small Catechism, Large Catechism, and the Book of Concord, with each book in series getting much larger and having more specific doctrinal material.  Even though the practicing theology of Lutherans spans crazy extremes, even the pastor who may be pushing the envelope against traditional doctrines is nonetheless apt to teach the Small Catechism to his or her students with pride.

Does every major faith tradition in Christianity ultimately have a catechism?
No most pentecostals do not have a catechism. Some churches do have introduction to the faith classes but there are no predefined standards.