Basically, a wireless router is an access point (AP) with router capability. Sometimes for some reasons you may not need another router to broadcast a network wirelessly. You need an AP and not a wireless router for broadcasting a local area network wirelessly.

Why?

A wireless router has different network ID between it's WAN and LAN connector. That's what routers are for, connecting (routing) two or more different network IDs (in this case: LAN network and WAN network).

Did you ever realize that someone on your network could steal your private data such as your username and password email? It is possible to do with a method called ARP redirect or sometimes called by ARP poisoning. This method is also often used by worms or spyware to hijack your private information gathered by those worms or spyware and sending 'silently' through internet to it's owner without you to be noticed. This is can be avoided by installing antivirus or anti-spyware that monitor and scan your network packet data activity on your network connections.

Actually you can't ping a specific port by using the ping command to test whether specified port is open or not. The ping command is used to test specified node/host whether it is live or not. It uses ICMP packets (wiki.answers.com). You can test a port whether it is live or not by telneting the port using the telnet command. The telnet command is a utility to connect over TCP and defaults to port 23 (make a TCP connection to port 23 on remote computer/server). But if you specify a different port than 23, then what the telnet command do is opening a TCP connection on the specified port to the remote computer/server.