Cigarette lighter not working and radio turning off - Renault Megane?

I have just bought a Renault Megane 55 plate and the cigarette lighter does not work for my satnav. My partner checked all the fuses last night and all seemed ok. This morning, the radio wasn't on when I turned the car on, I had to do it manually. It switched itself off midway through journey so turned it back on. When I turned the car off and opened the door the radio was still on, when normally it turns off, I had to switch it off manually. What is the problem with both? Thank you, Becca