I usually don't bribe if there is a general with the army. (exception is when I am either short on governors or really can't spend the cash I have)
But Parthia cannot really recruit anymore of those heavies, and you can add it to your army.
Without the catas, the Parthian sieges will be made of eastern infantry swarms only, which is no threat.
I should have said that I would only do this if I am attacked by Parthia early.
About Spain-Carthage-Cordoba bribe: I think that still is a good idea, the most problematic thing for me as Carthage is to train enough men to both defend the city and conquer. And iberians/roundshields led by a captain are not really expensive.
Well I usually don't bother with their desert provinces, and I don't attack them until they start a war.If this happens, you can invade their lands, but it's often not worth it for a while IMHO, because you wont destroy the faction, so they'll continue to send out armies until you march into the desert to take a settlement that you really don't need in the early game. With the same effort you might as well take Croton which would help a lot more to speeding up your campaign. Short sea trade routes are indeed the most valuable.
What usually happens is that they send a big, but crappy stack at Carthage, what will be defeated instantly. I create a small army (4-5 iberian inf, 2-3 roundshield, 1 elephant) and take their coastal cities, and train up garrison (3-4 units of town watch).
Even if they can save up some money to create a half stack army, and siege my cities, it is easy to hold out in the town square with the town watch forces.
(I never use peasants for garrison when some kind of militia is available)