Eastern Catholics, especially Byzantine Rite Catholics are very much just as Catholic as you and I. The Catholic Church is made up of 23 sui juris Churches which the Latin Church (ie Rome) is only one. Roman Catholicism is the largest demographic but is not the sole demographic that makes up the Catholic Church. The prayer rope preceded the rosary, it’s been around forever. Eastern Catholics are basically Eastern Orthodox in full communion in Rome. The reject the small number of false teachings separating the Orthodox with us Roman Catholics so they are 100% legitimate, you have no need to fear. And they absolutely DO have their own catechism and canon law. Some Eastern Catholic Churches don’t have their own particular catechism but my experience has been that most Byzantine Catholics, regardless of what specific Church they belong to, look to this as their guide http://catechism.royaldoors.net/catechism/
Canon law is only relevant to it’s specific Church. Roman canon law only applies to the Roman Church. Eastern Catholic canon law only applies to Eastern Catholics. They are certainly SUPPOSED to be following their own canon law because they are their OWN Church lol.