Simple wifi network at home - problem with ro

Hello!

I've got wireless network at home. In one room I've got PC (not laptop but stationary) connected to scaner, wifi router, printer.

http://images44.fotosik.pl/212/2d9aa5b7855b95a2.jpg <- I know it is not a profesional scheme, but I don't know how to use MS Visio.

I think there is physical problem with the router (I mean the network doesn't work properly and I think it is partially connected with settings but in most case with the device itself). How to check / proove that wifi router should be repaired?

I'd like to understand how this local network at home works from the beginning to the end - its physical and IP addresses, connections, protocols and so on. I want to do it because there are often problems with this network. When I reinstalled sister's laptop I couldn't set the internet connection again. I installed all the required drivers but I cannot connect to the network. I used to have access to this wifi network on PSP, but again - I can't access it, even if there were no changes made to network configuration on PSP. I also want to buy 1TB disc on USB, connect it to stationary PC and enable in the whole network so that all the users can have access to it. (Wireless access but also cable access - there is cable from the room where stationary PC and router are stored to the other room - we used to use this cable when there was need for fast sharing big files in the network, when wifi was too slow - however now this cable connection doesn't work). I've got sometimes some difficulties with accessing files shared on one laptop from the other laptop in Windows operating system. Similarly there are often problems with printing documents throught wifi - sometimes it prints it and sometimes it shows error about connection with printer.

Greetings :-)!