ok - here goes:
1. Military units cost a number of gold per turn to support. Some governments offer a number of 'free' units (i.e. no support cost) per city. It's all detailed in CivEdit under Rules > Governments
2. Sorry, I have no idea what you're talking about.
3. Bombard weapons (catapults, cannon, artillery and radar artillery) use a special attack in place of attacking normally. Pressing 'B' brings up a red grid which shows you the range of your bombard. Artillery units cannot directly attack units in the normal fashion but they can occupy undefended cities.
4. Culture is very important in civ3! First of all, if you acrue enough culture points bu building temples, cathedrals, etc. you win a Cultural Victory. Secondly, if your culture is high enough, you can absorb foreign cities into your empire - they overthrow their ruler and join you! You also need to be wary of your own cities switching sides if your culture isn't high enough.
5. No special defense vs. cavalry.
6. Depends on what is needed. If the AI hasn't discovered Sanitation (and thus can't buld hospitals) then their cities can't grow past size 12 so irrigation at this stage is useless.