Got a 98 buick lesabre for my daughter. It has about 90k. She put about 5k on it. She told me it was running rough. I drove it and it ran fine. It got hot though. I came home and the radiator and reservoir were empty. I put about 1.5 - 2 gallons of coolant into the radiator and reservoir. I started the car and it ran rough for about ten seconds, blowing white smoke from exhaust, then it died. I checked under the hood and all the coolant was gone. the coolant is in the oil pan. Is the engine done?

she blew the head gasket. Do this test to find out for sure  then probably junk it unless you know a good mechanic who can do engines. https://www.youtube.com/watch?v=QA7KVQq9vKA