Generally, if parties cannot agree, then they need to file in Court and have a judge decide. You may want to try mediation before you file in Court---and many Court systems require you to try mediation before the Court will hear your case.
If you were married to some one else at the time of your marriage to the 2nd person in the United States, your 2nd marriage is not valid under Virginia law. You need to be sure you are divorced from the 1st person and then you would be able to marry the 2nd person. Based on the facts as you present them, you are not married to the 2nd person under VA law.
Experienced attorneys generally charge more---but you need to be able to work with the attorney you hire, so meet with the ones you are considering and decide after an in person meeting.
it is not a matter of a lawyer knowing a judge but rather being known for being a good lawyer.
Generally, the Court will uphold an Agreement even if it signed before the separation period is complete (which is very common) as long as the conditions to uphold an agreement are met. You should probably consult with any attorney about your particular situation.
If you have no support order and no paternity established, you need to act on those fronts right away. HIs prior income could be used to impute income to him for support purposes, but that depends on a number of factors.
You should consult a lawyer about this matter and bring the mortgage, deed and any other documents related to the house to the consult. Depending on how the house is titled, you ay be able to sue your ex to receive the house, or a portion of it--but that may require selling the house.
The short answer is that you can file for divorce once one year of separation has occurred and either have him served where he lives (even if out of the country) or if you cannot find or serve him, have him served with the divorce by publication (which is an order of court and a notice in the newspaper). It takes a bit of time but you can eventually be divorced. The greater question is probably whether you will be able to obtain child support from him and any custody arrangements, but you would...
Given the facts as you have stated them, you should also obtain an attorney who is familiar with the Foreign Service and the special issues in divorce related to the Foreign Service. If you and your husband can cooperate and move forward, a collaborative or settlement process could work for you, but there is always the possibility of having to fight in court.
Consult with a lawyer to move this case forward. if there are any property or debt issues, those would need to be addressed but if not, you will still need to consult an attorney on the best way to file for a divorce, whether on grounds or separation, if you have been separated long enough.