In case i dont want to use the feature of "extend a network" but I want to use the one that says "use a wi-fi network". Does this network have to be apple router too or can be 3rd party?
As I said above.....
If the AirPort Express can connect to the modem/router using a permanent, wired Ethernet cable connection, then it can be configured to provide more wireless signal coverage that way.
So, this can be used with a 3rd party router.
How long is the range for the Express if I connected to the router that is in the basement?
The AirPort Express will have approximately the same range as your current modem/router.
You will need to run a long Ethernet cable from your modem/router to the area where you need more wireless signal and connect the AirPort Express at that location.
An Ethernet cable can be run up to 330 feet, or about 100 meters with virtually no signal loss, so unless you have a very, very large home, you should be able to locate the Express exactly where it will be needed.