If a city says it has -2 food that just means it consumes more than it produces. Food is automatically transferred from cities with surplus.

Only if you have global lack of food (ie - the top bar says minus rations) will your citizens begin to starve.  When that happens, a black round symbol with a fish skeleton will appear over your cities starving.

UNless you play on easy or normal, the AI is cheating with resources. A resource that would produce 4 food for you will produce 8-16 for them.

It is a band-aid for a poor AI.

Once the road has been constructed (the caravan has reached the target city) it gives a % bonus to food production. Unfortunately, it is rather easy to exploit at the moment, if you send a caravan from a city to another city far away you'll get a large bonus. Even if the caravan is destroyed, the bonus remains.

After the caravan has done a certain amount of runs between the cities, the bonus gets stronger.

When your global food is negative all of your cities go into "rationing." You can see this if you to the city detail screen and then click on one of the resources it produces (in the upper right of the detail screen, click on Gildar: 4.2 or whatever it says for example). In the sub-screen for that resource it will list a "Rationing" penalty of -50%. This -50% penalty applies to ALL resources, except Prestige which gets -100%. The penalty will remain until your global food becomes positive again.

Perhaps the Ai had researched refined farming to a level where they could support their cities? I know you can do that.