I just starting using this forum yesterday myself, but have been playing Civ3 for somewhere between 1 and 2 years...
Infantry, hmm...Well, they have a defense of 10. Here's some bonuses:
If they are on a Hill (+50%): +5 defense = 15
If they are on a Moutnain (+100%): +10 defense = 20
plus consider if they are fortified, that is another +5 added to the above. Considering the defense of the modern armour is not 24, it's understandable they will be destroyed at times. I recommend using artillery or bombers to bombard and weaken them first if you don't have an abundance of modern armour (which I would).
City improvements will also increase their defense, as well as other terrain, but hills and mountains are what you have to watch out for. I don't know if it makes any difference (I'm assuming it does), but I always attack from a hill or mountain if possible, to give my attacking unit a better defense
Shields, food etc...meh, I haven't really ever sat down and took notice of it. I will say this though, it helps a lot to have food bonuses. It would take a long post to explain everything about food here, but basically if you don't have more than 2 food per population member, the city won't grow. I recommend reducing the growth time by having irrigation on up to 4 grasslands (once you're out of despotism that is, or can irrigate a cow/wheat square).
As for shields, if you have 5 shields and 1 is red, you are only getting 4 production per turn. On accelerated production, you only need half as many shields as the building says it needs. (So 30 for a temple instead of 60).
Micromanaging cities....boooring...not my thing lol

I think you do it by going to the city screen, then contact governor buttone, then selecting "manage production". I've NEVER used it though! In over a year!!
When you have enough workers (e.g. 72-86+ in the industrial/modern age), then you can perhaps automate some of them, but the last thing you want is for them to go and build a road on a mountain that isn't near a city, or cleaning up pollution from an active volcano, or even going to the edge of your territory when you're at war. You should learn to move more than 1 worker at a time by selecting the "move all units of this type" button on the main screen.