Is my dad automatically the administrator of my mom's estate/

Generally the spouse is not automatic, two or more persons can be apppointed, and you are correct that appointment is made by a court but the law of your mother's state of domicile would determine the procedure. If your parents have a lawsuit the attorney handling the lawsuit might provide advice but that may be to your father and your interests as children may be different than your fathers interests so you might need to consult with an attorney not associated with the firm that has the lawsuit for your parents; the procedure for appointing someone in the lawsuit might be different than the procedure for a genral administrator when there is no will? Responsibilites on a foreclosure may depend whether the mortgage holder obtains or waives a money or deficiency judgment. Being aware of conflicts of interest with this number of legal issues recommended that you with an attorney who is licensed in the state of your mother's domicile, in the state where the suit is pending, and in the state where the real estate is located, whihch of course may be all the same state or different states.