I'm a convert from Roman Catholicism to Orthodoxy and I'm comfortable answering any questions regarding Faith or ecclesiology here.
To answer the question of universality, yes the Orthodox are Catholic in the fullest, deepest sense of Faith. Faith, not hierarchical affiliation, is what's considered to be the most substantive, unifying thing. Communion is based on a mutual recognition of a person/group/church sharing the same Faith, and is not on adherence to the hierarchy of one specific church. This same unity doesn't exist, as you probably already know, within the Roman realm, since you have Traditionalist, N.O., Charismatic, Eastern-Rite, Opus Dei, etc etc RC's. Within each group, different practices of prayer and Liturgy form the Faith of people differently, and the RC unity (based simply on "Communion with the Pope") is therefore only skin-deep. A person formed in one of these environments is likely to not be comfortable at a Faith-level with one or more of the other environments. How could the Pope be everywhere at all times to ensure that unity is maintained?
On the Orthodox side, I'll be comfortable at a deep level with most everything in the Russian/Serbian/Polish/Romanian/OCA/Ukrainian/Greek/Coptic churches, even if I can't speak the same language as all of them, and if we're not within the same hierarchy. The Orthodox Faith is universal.