If no one else is in the car except you (driver), then baby must be in the car seat, secure tightly. No, no need center back. Nowadays car seat are very advanced and trustworthy, can move in 360 degrees too, so it can be put at the side.
If there's someone else driving the car, maybe it's up to you if you want to carry or put in car seat. Sometimes, it makes sense we just want to relax for a short while and not always carrying baby.
Mik