The strut between the two headers is improving chassis rigidity, especially the torsional one (Domstrebe in German).
The anti-roll bar should be the metall bar, usually roughly shaped as an U, that connects the suspension linkage on the left and right side of each axle.
Changing one anti-roll bar can extremely change the handling of the car, I wouldn't recommend it either. Especially not without keeping an eye on the rest of the suspension.
The GT3 not only uses different anti-roll bars, shocks and springs than the std. 996, but several suspension parts should be different either. In fact the GT3 is, despite less equipment, heavier than the Carrera!
I have to agree with earlyapex that you should concentrate on your driving and that your car is in decent shape.
You might not find your limits on the very first track day so keep cool and don't spend to much money and time on the car in advance. In fact a modified suspension can make the car much more difficult to control so better stick to the std. susp. first!
Try to find someone very experienced and ask for a ride - you might figure the difference to your own driving pretty soon... And don't try to copy his or her driving style and cornering speeds right afterwards, because there is way more about driving fast than mashing on accelerator and brakes!
Anyways, have a lot of fun! Greetings!