@hiyadews,
Hiyadews: Welcome to the world of long-distance relationships. There is a reason why they fail so often. Regular relationships are hard enough because so much communication gets misunderstood: if your main mode of communication is Facebook, then you're bound to have problems.
Why do you want to be with this woman? You should take a long, hard and scrutinizing look at your real feelings and motives. Often, in international relationships, the main reason why you are actually attracted to the other is simply the novelty of being with a foreigner: even mundane bits of information about the other seems exciting because you not only evaluate the other person, but a totally different nationality as well. You might also be infatuated with the idea of associating yourself with the foreign country, which makes you feel renewed and special.
Anyway, from reading this, I have three opinions:
1) Breaking up is unavoidable, no matter if it's today or in 3 years when the novelty had worn off and you realize you are in a relationship with a woman whom you can't trust.
2)You do seem like a jealous and demanding type of fiancé. There are plenty of women who do not mind that you are going through their social media acquintances or timing their meetings with their friends, or who want to spend 24/7 with you on Facebook when you're not around each other. Clearly this is just not the optimal situation for your Russian lady, and she's starting to get bored with this lifestyle. She probably has a relationship with a co-worker because unlike with you, she actually spends physical time with this guy every day. That can become a very attractive option after living your life online for a year.
3) If you two spent more time with each other, it's likely that you would notice you are not meant to be with each other anyway. When you're in a long-distance relationship, you are actually dating a self-created fantasy that's occasionally supported by real, live sex. Once you actually move in together, you crash down hard when your fantasy shatters, and even the smallest things about this stranger that you're now living with becomes unbearable. This is why I recommend that you do not ask for her to quit her job and move in with you to another continent because it's likely that you will both regret it (unless she really wants to move to the US anyway).
I'm wishing you guys luck, but as somebody who has experienced a long-distance relationship with a foreign guy, I can safely tell you that while it was an interesting time of my life, I really don't miss the actual relationship or the guy in question.