I'm Lucy, and I'd be happy to answer your questions today. I'm sorry to hear about your situation.
1. Get a copy of the official marriage license from Korea, and take it to the Korean Embassy in the United States. They should be able to give you an apostille, which is an official translation. That document can be filed with the New Jersey courts when you request a divorce. Because you are a US citizen living in the US, you do not need to file anything in the Korean courts unless you intend to move back there and need to be sure they recognize your divorce.
2. Yes. If you do not pay the mortgage, the bank will foreclose, and it will destroy your credit. When a person signs a mortgage, their obligation to pay is never based on living in the house or being married or anything like that. As far as the bank is concerned, you're required to pay until the house is sold, or until your husband is able to refinance in his name only. This is true even if your husband gets the house in the divorce - if he doesn't pay, it'll go on your credit because the loan is in your name. If you don't think he can or will make the payments, you can request that the house be sold as part of the divorce.
3. Possibly. Alimony is need-based, and it's typically reserved for marriages of 10 years or more. Your husband has a right to continue the same standard of living he enjoyed during the marriage. If he makes enough to do that on his own, it's possible a judge could deny him spousal support. If he asks for alimony, you could ask the judge to be allowed to deduct his share of child support from the payment before sending him anything (rather than sending him a check each month and waiting for him to send one back to you). Another option is to see if your husband will enter an agreement where you both agree that he'll pay $X in child support, you'll pay $X in alimony, and no money need change hands each month. Before doing that, use this calculator to find out how much he could be ordered to pay you.
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