To make it short. Yes you can commute by car within Germany very easily.
Where do you live? If there is a flight, you can even jumpseat.
There is no typical roster, on the flex roster you can get something like 5-6 days on and 3-5 days off, but as its says, its flexible.
After some time you can also go on the block roster, which is more or less 1 week on 1 week off.