<<<< I wanted to know can I have the wireless router situated downstairs at my telephone connection but not connected to any computer and connect my PC upstairs to the net. >>>>
Yes, you can but the quality of the connection will be dependent on what lies between the router and the PC, in particular the composition of walls & ceilings through which the wireless signal has to pass.
<<<< P.S My PC does not have a wireless card, do I need one? >>>>
Yes, you will in order to connect wirelessly to the router. This can be either an internal PCI card or a USB WiFi adapter.