"A resource is connected to the trade network" means an appropriate building was constructed on that resource and it may now be used or traded to other civilizations. Trade routes are about connecting your cities to the capital by roads and harbors and then generating gold automatically from the connection. Trade network and trade routes don't have anything to do with each other.
A great person's improvement can connect strategic resources but not luxury resources. The type of the improvement does not matter - a manufactory, a landmark and a custom house provide the same amount of iron when built on an iron resource.
The reason great person improvements are allowed to connect strategic resources, is that strategic resource aren't revealed on the map until the cooresponding technology is researched. It would be a disaster to require someone to tear down their landmark just to get to the Aluminum that appeared underneath it.
Luxury resources are shown at the start of the game and so this grace in the rules does not apply to them.