I have some questions about single player if anyone can help

In the Way of Chi the Sumo Tournament states that in consumes food 1. Does that mean if there is a food shortage that it is going to reduce the food further? I usually have quite a few rebellions due to food shortage.

When an army has some depleted units is the replenishment rate contingent on the facility that is closest to it?
Example If that army is in a province with a spear dojo and there is a sword dojo three provinces away will the yari units replenish faster then the sword units?

I'm also having a problem still with Christianity. I've noticed that when I've taken over a province I will put a monk or two in it. Christianity will go on the decline, an as soon as I pull out the monks Christianity goes back up. I don't have one of those trading ports which will causes an increase in Christianity, so I'm stumped on that one.

Thanks