Welcome back to JustAnswer.
Wow, what a mess! My primary thoughts are with Kim's 14 year old daughter. I hope she has gotten her some counseling. To answer your questions:
1. Did she violate any law by dropping the charges in exchange for the financial assistance? They give her $3000 a month and allow her to live in the Marital home. Would this be considered an out-of-court settlement.
Yes, this could be considered bribery. It is a crime to offer a bribe, and a crime to accept a briber. Legitimate out of court settlements are only done in civil cases where the parties are suing over money. They cannot legally be done in criminal cases.
2. Since the family did not put the agreement in writing, is an oral contract valid? The $3000 a month should prove an agreement was reached.
Regardless of the written or oral nature of the contract, illegal contracts (i.e., contracts for the sale of drugs, gambling contracts where gambling is illegal, and bribery contracts) are unenforceable. No way to enforce an illegal contract such as this.
3. If an oral contract has been created, is it Enforceable?
See previous answer.
4. Can she still prosecute since they violated the agreement?
She can still seek prosecution. Depending on the circumstances of the rape
the statute of limitations is likely to be three or four years after it was reported to the police. However, it is much less likely that the State's Attorney will prosecute the case now that it has been dropped without additional evidence. The monetary agreement other than probably being a crime destroys Kim's credibility and to a great extent her child's credibility because people (jurors) assume a parent can and will coach their children particularly where money is involved.
5. Can she be forced out of the Marital home since it is not in her name? She has lived there for 4 years.
My area of expertise is criminal law not property or family law. I would ask that question in the family law forum. Having said that she does not have to abandon the house based upon their phone call. They would have to go through the legal eviction process which she could contest. It may be that she is entitled to the home or at least a portion of its value.
6. Are there any steps you would recommend she takes to secure the well being of her children?
That is a tough question. She obviously needs to keep them from people who would hurt them like her husband. Secondly, she needs to get her daughter into some counseling if she has not already, and most importantly be supportive and stick up for her daughter and other children. Financially, she may have to seek government support such as welfare and food stamps
7. If she tells the rapists' family, that if they stop assisting her and the children, she will reopen the case, can she be considered to be blackmailing the family?
Yes, that is blackmail or extortion. She absolutely should not do that. There can be no tie between money and criminal charges except in some financial crimes. Not only is it illegal, it is morally reprehensible. Most prosecutors, judges, and jurors would not hesitate to imprison a mother who sold her daughter's rape charges for money.
I have recommended she speak to a Korean-American attorney as they would understand the cultural reasoning as well as applicability of US Law. However, I am unsure what the attorney should specialize in... Family Law? Criminal or Contract?
I agree with the Korean-American attorney if for no other reasons than the language barriers and her own comfort level. She does not need a contract attorney. I would suggest primarily a family law attorney to address the issues of what marital assets including the marital home she may be entitled to. Many family law attorneys do some criminal work and vice versa so ideally she can find one who has experience doing both.
I commend you for trying to help your friend, and I wish your friend and, more importantly, her children good luck. They are going to need it.