2005 Buick Terraza 2005 Terreza

I recently bought my 2005 Terreza and have had a few unsual things happen. The radio goes off for no reason and then when I get back in it to start the radio is on. This happens a few times during a week. The other recent thing is it does not start right away. It usually takes a couple of tries before it will start and the most recent thing today is I filled my tank and it registered full at first, then later on it was reading low fuel and the marker was done on empty with the light on. Then I started it up again when I got home and it was registering full again. The last two things both happened today when I was shopping. Could the battery have something to do with these problems. Should I have it serviced where I bought it or what should I do. I need this vehicle working properly by Wed morning as I am picking up my granddaughter and daughter at the airport and I don't need car problems. Please any advise you can give me and are these vans noted for these problems. Thank you.