Caesar, I believe it means Champion. It is the what the Parthians called themselves.

I was wondering if the Pahlava will have the same culture as the cities of Seleucid controlled persia. I thought it was very unrealistic to capture persian cities that were completely Hellenized. But then how will the Seleucids be able to hold their empire together with it being so vast and still have the culture penalty?
Well, they are not the same culture as the Hellenics. However, Parthia did adopt a good deal of Hellenic culture, and many Greeks were far more comfortable with them than the Persians were of their fellow Iranians.

BTW, what's the difference between the Zradha and the Azad cataphracts? Is one more 'elite', or are they just different units?
There were many variations of the cataphract type. Each noble provided their own equipment, which pretty much meant that no two cataphracts were the same. However, as we can't do that, we have multiple types of cataphracts. The Azad I believe are the second highest cataphract. They would be more expensive and be of better quality of the Zradha.