Center Tapped Transformer secondary winding direction
If it is 'same direction' would it have any relation with primary
  windings direction?


The two windings are wound in the same direction just like this little ferrite wound component: -



If the centre-tap wasn't there the orange and red would be one continuous winding in the same direction.

The direction that both have in reference to the primary winding is of no-importance for AC power transformers but, in other applications like transformer fed loudspeaker arrays it would make a massive difference at bass frequencies if one transformer had the opposite phase to another.


  Also, is there any change required in terms of winding direction, if
  used in a Full Bridge inverter?


No.