No, generally they are set to automatic and find the channel with the least noise, I believe in the USA we can use channels 1-12 on the 2.4 ghz frequency. Also the 5ghz (N or A standard) have ALOT more channels they can use (I don't know them off the top of my head). Some older routers may just have their default channel set to 1. Keep in mind generally there is channel bleed over with these so if you set channel one it may also interfere on channel 2 and 3 so set them far apart (IE: 1 and 11).
Yes I have not seen any wireless routers that don't have this capability however they may exist so don't buy a cheap knockoff, any linksys, netgear, D-link ect should have this functionality.
They search all the frequency's for any broadcasted SSID (wireless network name).
Yes, wireless networks operate in half duplex. Meaning if one channel is sending data OR receiving data nothing else can use that channel simultaneously not even the same device.
Yes and no. They may not be actively transferring data and may leave the channel clear for a few fractions of a second but as long as it is connected it will be replying and sending ARP info as well as responding to other requests over the broadcast. Networks are busy even if you aren't using them.
Additional info:
Make sure only one device is providing DHCP and NAT. The second wireless router should only be acting in layer 2 mode or access point mode. Double NATing may work for a bit but you will run into problems with network traffic that relies on UPNP (games, bit torrent, skype ect) it may also cause random issues on your network.
so there can be found by the PC more than a single SSID using the same channel? – Vass – 2011-10-12T16:11:43.193
1Yes, there can. In fact just in my office building there are 4 wireless networks on channel 1. Remember only one can communicate over that channel at a time and the stronger of the signals will take precedence. – Supercereal – 2011-10-12T16:47:05.397