I get that the party has hunger but is there any way to check their hunger or anything? or do you just wait till they say they're hungry?

and the screen keeps going different colours, is this the night/day cycle?

There's no way to check how hungry they are, but they won't eat if they're full. If you have a lot of food have a feast.
edit: actually there's an icon in the stats window that shows if they are hungry. See the reference card for more info.

There's night/day cycles as well as random weather.

If they have food in their inventory will they automatically eat it?

I don't think so. I store extra food in their inventory and it's never happened. Maybe if they're starving.

Maybe the people of Britainia have become too dependant on the Avatar.