With all else we are able to see, would we be able to see food surplus in the embassy screen. We can see their metal and coin, after all. Would let us know if offering food as a bargaining chip would be welcome. Starving warriors will trade victory for a loaf of bread...

Food isn't currently a resource that you can regularly trade, so you can't offer it unless they ask for it.

But should not it be though. Of all the things I get requested food is very common, almost the most common (that and metal). Diplomacy options are adding a fair bit to the game, looking forward to the tweaking of it.

Food trades would have to be per-turn, since food can't be stockpiled like metal, and this makes it easy to get into trouble if you're giving out all your food and your own internal consumption grows.

The food requests were meant to be an infrequent thing, and so the frequency of requests should be dramatically reduced. The event system wants to fire off events, and the current build has only a few to choose from, so you're seeing the same ones over and over again. We're adding more.