I've not used eagle all that much, so I'm a newbie, too.
But, a net can have just two things connected to it. The software seems to handle nets better than wires, terminating them when a connection is selected, and joining them when an existing net is selected to end the wire.
Wires can be used, but ending the wire and joining it to others to form a net are not automatic. Simpler to just use nets.
If you have both the schematic and board windows open, and you connect to connections together, you will not get a trace in the board window. You will get an air wire. Air wires get converted to traces using the Auto-route command or manual trace layout techniques.
Traces on the board are not reflected on the schematic. You need to create something to trace (in the schematic) first.