Hello,
group.getCartesianPath and group.plan will just display the planned trajectory, by default in a loop.
If you want the trajectory to be executed, then you must call group.execute(plan).
group.getCurrentState will return a RobotState which can be used to get position of any link.
It doesn't exactly execute the plan when you do group.plan(&plan). It just displays the planned path. The state of the robot is not changed.
I guess you could turn off the planned trajectory display from Rviz settings checkboxes.