As an American lawyer, let me tell you a few things--none of which constitute advice rather information for you to consider. As you will see below, each state of the US has its own laws, so many specific answers about the rules are dependent on the jurisdiction. But, immigration law is a federal matter and the states have no role to play.
Although each state has its own specific rules, legal foreign marriages are generally recognized in the US. All this means, however, is that the individual is considered married. (I.e. the recognition has almost no immigration consequences.) Remember it must be a legally valid Dominican wedding to even pass go.
Although the process for petitioning for either immigrant or nonimmigrant status for your friend must be started by her spouse and will take a long time, it actually requires substantial information that the husband will have no access to without her involvement. Also, for a certain status the petition must be made in the Dominican Republic, so it would appear that your friend has lots of information already about the likelihood that the process has begun. (see the immigration site below for specifics).
On the prenup, two issues arise:
(1) does the US jurisdiction in which it is supposed to be enforced recognize this type of agreement? (Most recognize some such agreements, but many limit it severely. And some don't recognize those from other states or countries.)
(2) Can the individual seeking to enforce the agreement prove it is a validly and validly executed document governed by Dominican law that should be recognized in the state. This is a complicated, case specific question, that must be handled by a lawyer. But it basically involves asking whether prenups are valid in the Dominican Republic and whether the American husband can prove the prenup was validly executed.
Note: otherwise valid prenups may be invalidated to prevent extreme hardship to one of the parties or may not be recognized because they were unfair.
As for inheritance... again this is a state specific question. However, most states in the US have a law that states that the spouse of an individual dying without a will will take at least some (and, at times, all) of that individual's property. Where that spouse lives and citizenship is irrelevant, except to finding her. If her husband has a will, it will generally be followed--including if the wife is given nothing. However, most jurisdictions also allow a spouse who is not allocated anything in the will to contest the will and receive a statutory portion.
Finally, her divorce options depend on the state where it occurs. I have not heard of spousal support being denied because the individual lived out of state/country, but it would be rather difficult to monitor and enforce. On the other hand, if the prenup is enforced and includes a provision that eliminates spousal support, she will not be able to make the claim.
See these places for more info. It obviously is from the perspective of the American in the marriage, but they explain the process:
Marriage of U.S. Citizens Abroad
Spouse and Fiance(e) of an American Citizen
Divorce Abroad
Marriage to a US Citizen
Final note: US law, unlike the civil law, is HIGHLY dependent on the particular state, and the particular facts of the case. It is not wise to gauge your prospects without first consulting an attorney with experience in the relevant field, in the relevant state. (I'd say you need an immigration attorney, a matrimonial lawyer, and an estate planner practicing in probably New Jersey to give you a more accurate picture of your friend's situation/prospects.)
aranoid: