It is a simple procedure, BUT you absolutely should consult with an attorney to discuss Estate Tax planning. Adding the name to the deed may be what you think you want to do, but may NOT be what's best for your or for your parents' depending on so many different things. I therefore am NOT going to provide "DIY" instructions.
If the lawsuit is in NY the answer must be filed within 20 days if you were personally served and within 30 days otherwise. Weekends do count, except that if the last day falls on a day the court is closed it gets extended to the next court day. If you were covered by insurance you should report the claim to your carrier.
You have no obligation to pay any debt that was discharged. Either the lender or the condo can foreclose on their respective liens. No one can come after you later for a debt that was discharged. The foreclosure process can take months to years.
A lawyer is not necessary to make an offer, but a lawyer who is experienced in short sales will be an asset going forward. The process is a long one and you will need patience. While you are under contract the house may not be sold to anyone else, but you are far from guaranteed that the house will be sold to you, even if you have the highest bid. Make sure your lawyer leaves room for you to get out of the contract if there is no response from the mortgagee by a certain date and that you also...
If you had a lawyer representing you on this purchase he should be the one to advise you. If he does not do litigation, then at least he will know the facts as to whether the contract provides for return of the down payment. It sounds like the commitment was conditional, but the facts and contract must be further examined. The best answer I can give to you is 'maybe."