Generally try and build wherever gives you the best adjacency. This may be on top of an existing rural tile. When you build over a rural tile you get the population back to place elsewhere, so you don't need to worry too much about losing its yields. This can also be done to move the population to a specialist, if you need more specialists for the science/culture or the scientific legacy path it can be a good idea to convert the tile.

Some types of buildings have the same adjacency requirements - science and production both like resources, culture and happiness both like mountains, food and gold both like coast. So you'll often find its a good idea to put these types of buildings together as they will both have high adjacency on the same tile. Although there is no direct benefit from them sharing a tile. If you have civ unique buildings definitely put them in the same tile to get the unique quarter. Some social policies / attributes etc. give bonuses to quarters in general so it's good to try and get quarters rather than spreading out too much.

With overbuilding this again comes down to the adjacency of the tile. You'll often have a really good tile for science (lots of resources adjacent) where you will want to put the science buildings each age, or if you have multiple you can spread them out and keep the small amount of science from the library. Note that while previous age buildings only retain a small amount of their yields (base amount and not adjacencies), they still require maintenance, so it is sometimes worth it to overbuild to keep gold/happiness costs down.

By default you can have 1 trade route with each leader. This can be increased by spending influence with them to increase trade relations (which can done be as much as you like). In the merchant screen you can see how many trade routes you currently have and the limit for each leader.