What is required for the ball handler to have established himself in the frontcourt? I thought both feet and the ball had to have crossed the center line. If just the ball, one foot, one foot and the ball, or even both feet without the ball have crossed, then the player can return to the backcourt without being called for the violation. Is that right?

That is correct... both feet and the ball have to be in the front court before a violation can be called for going back.