City and Resource management

I was playing against AI last night. I checked the city details and found food production was 0, why that happened? Had I not checked I would not have discovered that. How do I prevent that?

When you're producing a Settler, your city automatically stagnates. During this time, EXCESS food is converted to production. The exchange rate is that the first, second, and fourth EXCESS food are one hammer each, along with one more hammer for every four food after that.
 
May be it is still a bit too early for me to jump to that comments. But having said that, I find Civ 5 governor's decision is neglecting food production leading to 0 food production making next citizen taking hundreds of turns!?!?

It also happens to hammer as well.

Also, when I was battling, my gold could go negative making me losing the chance to produce an atomic bomb to save the world.

If I follow the default focus, then I just click next next next....?

By the way, I notice AI builds trade post in late game, should I also do that?
 
I find Civ 5 governor's decision is neglecting food production leading to 0 food production making next citizen taking hundreds of turns!

That should only be happening if your happiness is in the red. The default governor pays fair attention to growth. But maybe you settled poorly?

It also happens to hammer as well.

That is more common. It should not be a problem once you build a water mills or improve pastures and camps.

Also, when I was battling, my gold could go negative making me losing the chance to produce an atomic bomb to save the world.

Now your are talking late game -- you money problems should be well resolved by then!

If I follow the default focus, then I just click next next next....?

You should have plenty to do without micromanaging city screens. Do not automate scouts or workers. You can switch to production focus when the science buildings are in the queue, also for Wonders and International Projects. Switch to science focus for 8 turns leading up to bulbing your GS.

By the way, I notice AI builds trade post in late game, should I also do that?

No, absolutely not. The easiest rule of thumbs are: TP on flat jungle. Farm everything that can be farmed. That just leave dry hills which should get mines.
 
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