Yes, they can.
You cannot legally marry if your divorce is not final, even if you go to another country it is still bigamy.
No. I don't think it would be legal. I know people go to Mexico for divorce, but there is special paperwork and requirements that they meet. But, if you wanted to go to Germany for divorce I don't think you could. The laws there are German, not American law.
I do not think they can. I doubt that the state (or the country) will recognized the marriage of two illegal immigrants who married in another country. After all as far as the government is concerned "they are not here."
You already have a husband and just because you want another husband unless you divorce your first husband (at least in Western Countries) then you would be a bigamist which is against the law. File for your divorce; get the divorce and you are free to find another husband.
If you get married in another country, you have to have a ceremony in America. You should get married in the state you live in to meet residency requirements.
If you are now an American Citizens, it does not matter where you were married, you would file for divorce wherever you live, because your home state or your wife's home state would have jurisdiction over you and therefore your divorce.
You file for divorce in the country or jurisdiction in which you are living. Where you got married does not matter.
Your divorce in another country is legal in this country. Just make sure all documents are translated to the English langauge and are accompanied by a translators certificate of translation.
Yes. No matter which of the two countries you were married in, you are married until one of you dies or you get a judgment of divorce signed by a judge. You can still divorce your husband, even if he lives in a foreign country. You can still divorce your husband, even if you cannot find him. You cannot legally remarry until you obtain a divorce.
No. However, most countries (and states) have a residency requirement for divorce. That means, you must live in the country (and probably the state) where you file for a divorce for a minimum amount of time before you can file there (usually one year in the United States). Also, in the case of a same-sex marriage, you must file for divorce in a country (and state, in the U.S.) where your marriage is legally recognized - - not necessarily the same country (or state) where you were married, but one of the countries (and states) where same-sex marriages are recognized. Again, you will most likely have to satisfy a residency requirement.
It would probably be easiest in the country where you were married. Also, if everybody is in agreement, get an "uncontested" divorce. They are much easier and cheaper.