Fort upgrades cost food. Markets above the first one cost food.
The general rule seems to be to build as little as possible above the base level to keep food in surplus.
Surplus food contributes to the "growth" of every city you possess; that growth gives you gold.
"But we need castles!" "They're bigger and better!" Just not many of them; early game one upgraded castle might be all you need.
Farm upgrades give you gold and food; one of the best upgrades for your economy.
For religion, buildings and agents convert regions. I think monks/missionaries are 0.5 bonus /star; the building bonuses can be found by mousing over them. In the castle display there is a box showing the relative str of each religion; if you mouse over the arrows it will show the influence of each factor. Check the buildings: if their is a competing religious building => destroy it. If you can build one of your own temples it will help. Nanban ports boost conversion to Christianity by 3.5...but their economic benefits might make this tolerable.
Replenishment I understand not at all :p Roads and encampments help, but there seems to be more to it than this :) gl
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