Hmm...I wonder, when we pray the Rosary, should we pray for the conversion of Russia?
I'm assuming you're being argumentative, and so my responses are in response to that assumption. Since you're post is rather cryptic I'm forced to assume, so if your intention was a legitimate question, I apologize for my upcoming thoughts.
1.) Where does the actual prayers of the Rosary ask for the "conversion" of Russia?
2.) You are aware that the "hail Mary" (ie: O Theotokos and Virgin, REJOICE O MARY FULL OF GRACE the Lord is with thee, Blessed art thou among women and Blessed is the fruit of thy womb, for thou hast born the savior of our souls) prayer originated in the East? it's the same prayer used in the Dominican Rosary, just the Latin version is somewhat shorter, and asks for Mary's intercessions which can never be wrong, even if it is "western".
3.) Considering the reference I believe you're referring to (one of the Western Marian apparitions in the early 20th century I assume, as I've never paid that much attention to those nearly as much as many Orthodox seem to do) took place when "Holy Russia" really wasn't all that "holy" anymore, so sure, we should have been praying for the "conversion" of Russia. Why not? and why not pray for the conversion of all peoples even those in so called "Orthodox nations". Just because a nation has it's official religion as Orthodox Christianity, doesn't mean the people are in any less need a conversion of heart. I personally don't accept some ultra-traditionalist Catholic interpretations of those apparitions, (that Mary said Russia had to become Roman Catholics) but if you want to, feel free.
4.) The Rosary predates said Marian apparitions by many, many centuries, and the prayers themselves go back to pre great schism time. No Catholic is bound to accept those apparitions so why would an Orthodox Christian pay attention to them?
5.) A famous Russian saint prayed the Rosary, with the eastern version of the hail Mary, so what's the big deal? A Hail Mary, an Our Father, the Apostles Creed, and a couple closing prayers? These are all completely Orthodox prayers and Creeds. If one is uncomfortable with "hail holy queen", just substitute "it is truly meet to call thee blessed"...which I often do because I know that prayer by heart.
One can pray the Rosary in the same way we pray the Akathist, & the Paraklesis etc...we don't have to accept Catholic theology or apparitions that even Catholics aren't required to accept, so I just don't get the problem other than some unfounded fear or some "eastern good", "western bad" mentality.
I know a lot of people who DON'T pray the Rosary and that's cool. It's a personal devotion like the Jesus prayer (no one is required to pray that either, and as is often said, no one "chooses" the Jesus prayer, but people are called to it.)
I personally find the idea made popular in some theological/mystical circles that the Jesus prayer is "the best" prayer for everyone
a bit strange. I find the idea that a few Catholics say the Rosary is "the best prayer" for everyone a bit strange as well. But the question was simply is the Rosary itself acceptable? Considering even in Catholicism there are various versions of the Rosary (not just the Dominican Rosary we're all familiar with) I don't see why an Orthodox Christian cannot change this or that thing they might not be comfortable with if they so choose.
I personally love the Akathist Hymn (it's one of my favorite services in fact) but I cannot memorize the entire Akathist and pray it before bed, or in bed, or if trouble comes...but I can pray a hail Mary and a short decade of the Rosary, by heart. I can do the same with the Jesus prayer as well, but to me, these things are 2 different types of prayer. One is intercessory in nature, the other is a means of drawing closer to Christ, a way of inner transformation. They both have their purposes in my spiritual life, though neither holds a big place in it.
I know there is a lot of theological opinion built around the Rosary, much of it I'm uncomfortable with, but the prayers themselves are just as Orthodox as anything in a "eastern" prayer book. So to me, and obviously many others, including St. Seraphim of Sarov, it's just not that big a deal. It is to others, and that's fine too. Just don't pray it. And as Douglas said, its best to ask your spiritual father and see what he says, after all, he'll know you better than anyone.