I can only give a partial answer.
I haven't seen the archer tower target a catapult before, usually just the regular troops. That could be why they are not very affective. But if they do shoot at catapult, towers kiling troops works by population of the attacking unit. So it would take 8 towers to kill a catapult, or 3 to kill a knight, or just 1 to kill an archer.
The Ibero boost on city defense works like this:
It will give up to 10% bonus no matter what to the defending armies. This includes your wall, towers, and ballista. The city wall will also give a bonus, but can get knocked down by the catapult.
Also, the HP of towers is separate from the HP of your walls. If many catapult armies attack, they will knock down your towers after the walls have been reduced to level 0.