1. Sending internal trade routes will provide a rather significant amount of food, especially water routes (note that internal trade routes don't take away food/production from the city that is sending it). I usually use all food internal trade routes but there are a few reasons why someone might use production internal trade routes or international trade routes:Several questions, which I thought might go better here than in a bunch of new threads:
1) This past game I did a caravan to my capital sending food, and it really grew bigger than normal. Is that really the trick, sending a caravan helps that much?
a. Do you send it throughout the game or do you stop at some point?
-I actually needed more hammers in my capital mid game so I changed it from food to production.
2) Do you guys tend to colonize or not?
-Frankly, with the outpost mod, I see little reason to. I find it slows me down unless I am deliberately playing wide.
Production: I mostly use this if I had a growth heavy production light coastal or island city and I switch most of my food trade routes to production trade routes close to the end of the game where the longer term investment of food matters less.
International: There are a few reasons to use International Trade Routes:
Gold (obviously): If you are going for a diplomatic victory or you are otherwise in need of gold, International Trade Routes can help.
Science: International Trade Routes gives an empire science bonus (meaning that it is added directly to your cumulative empirewide science and is unaffected by bonuses like rationalism opener) to both civilizations in the trade route based on half the number of technologies that the other civilization has researched that the first civilization has not. Early game on higher difficulties, when your opponents are 4+ technologies ahead, this can be a very significant science bonus. (I believe you also will receive a few beakers from trade routes to civilizations that you have some degree of influence over, but that comes late enough in the game that it is irrelevant)
Religious Pressure: International Trade Routes will spread religious pressure to both civilizations involved in the Route which can be useful for spreading your religion outside of the normal 10 tile pressure radius.
Tourism: Having a trade route with a civilization gives you a +25% tourism multiplier which is useful for cultural victories.
City-State Diplomacy: City-States will occasionally give quests to send a trade route to them which gives you a significant tourism boost. Additionally, the Treaty Negotiation tenet in Freedom will give you influence for having a trade route to City-States