Arthur & Anna

Ah, I understand.
The Consulate may not have fully appreciated what you were planning on doing, or they were aware that it would be unlikely for her to get a tourist visa to the US, especially when you two were planning on marrying in the US. US foreign officials always suspect potential immigration fraud - that once she was there the two of you would plan to remain in the US and apply for her green card at that time - so set the requirement that she needed the K-1 even to enter the US. It isn't actually an accurate process for your intentions, but then they are the ones who set the hoops and tell you how high to jump. Suspecting that might have been one of the consideration, that is why I phrased my first sentence as I did . . . 'that you don't necessarily need a fiancee visa to do that'. The 'necessarily' was in consideration that the Consulate may not have given her a tourist visa under any circumstances so the only way for her to get to the US would be with a fiancee visa.
It is unfortunate that you were made to spend that amount of money and that amount of effort for what should, in fact, have been a tourist visa. Still, there is no reason why she cannot enter on the K-1, get married and then the two of you leave before the 90 day period authorized by the K-1 entry expires. Since your plans are to live permanently (at least for now) outside of the US, it is not only pointless to apply for a green card, she would also not be eligible. Green cards are for people who intend on living in the US - so you at least save yourself that amount of money.
If and when you do decide to return to the US, you would be able to repeat the process by what is known as a DCF - Direct Counsular Filing - of the I-130 petition. In the meantime, if you are both residing in Russia, own property, have jobs and other evidence that shows your intentions to return to Russia, she should be able to qualify for a visitor's visa more easily in the future.
Good luck to you.

Well, in many ways you have probably wasted the time and money spent on getting a K-1 visa. The visa is good for a one-time entry to the US for a foreign fiancee of a US citizen to enter the US for the purpose of getting married and applying to remain in the US. There is certainly nothing wrong with applying for the K-1 visa entering the US and getting married and then leaving the US, but you didn't necessarily require a fiancee visa to do that.
If your 'wife' leaves the US after entering on a K-1 visa she will not be allowed back into the US unless she has either her green card (AOS) or a travel document known as Advance Parole (filed for at the same time as the AOS application) or a CR-1 visa. Once the K-1 is used it is over and done with - there is nothing there to be used again.
In order for your wife to return to the US you would need to petition her for an IR-1/CR-1 spousal visa. You would start this by filing the I-130 petition either in the US or at a US Consulate overseas if you are legally living in that country. She would have to redo all of the security checks, medical exams, you would have to provide the same financial information and she would have another interview.
Yes, your passport needs to be valid in order for you to return to the US. If it is due to expire during the time you expect to be away you should go ahead and apply for a new one now. That way you won't have a problem re-entering the US, even though you are a US citizen.
I am not sure why it is necessary for you to move back to Russia right away, but if you chose to remain in the US long enough for her to get her green card, she would be allowed to travel outside of the US for up to one year and still be allowed to return to the US with you (as long as you don't intend to reside overseas and this relocation is temporary). If she planned to be outside of the US for more than one year then she would need a special type of travel permission and would have to return to the US before 2 years are up. If your planned time in Russia is temporary, you may wish to consider delaying your plans to move at least until she gets a green card so you don't have to go through the whole immigration process all over again the following year. The CR-1 process itself takes about a year so you would almost need to apply for it shortly after you leave the US if you wanted to return a year later. If you don't intend to live in the US for a while, then there is no need for any type of visa.
You are making it very complicated on yourself. If you have room to consider other options, you may find it much more sensible to delay your year outside of the US for a few months so she can get her green card.