The LAN port is not used for a dial-up connection. A modem is used for a dial-up connection.
Depending on how old the modem is, it may connect to the serial port, the USB port, or an internal connector.
It's not that it makes the Internet respond, it makes your DSL modem respond. Occasionally DSL and Cable modems will become unresponsive for whatever reason. Disconnecting and reconnting the Internet connection cable is one way to "wake up" the modem. Often that doesn't work and you have to reboot the computer or power-cycle the modem. Annoying but sometimes necessary. The way my ISP, who gave me my DSL modem to use, explained it is that, like a computer, every now and then, the modem just needs to be reset or rebooted, much like your computer
You cannot connect an RJ11 cable to a RJ45 port. You can buy an external dial-up modem, though, that connects to a USB port. A link to where you can buy an external USB dial-up modem is below. http://www.amazon.com/Small-Compact-Lightweight-Modem-Connect/dp/B001C4EUFE
A local area network card allows your computer to connect to other computers. You need a LAN socket if you want to use high speed Internet. If you want to use dial-up, you'd need a dial-up modem. However if you use cable, fiber, DSL, or satellite Internet with a regular PC, you will need a LAN socket unless the modem used with the service plugs into your USB port.
People are what will wake up a computer and remind it what to do. It cannot read a human's mind.
According to Wikipedia wak on lan is a family of networking standard that allows a computer to be turned on or woken up by a network message. WOL is the abbrevation of wak on lan.
If you connect your modem to the router, and then using one of LAN port (router's) connect the PS3 to the router, you will not interfere with wireless signal at all.
Maybe you have used up all your data on your home internet and don't want to connect to it
Plugging something in (or removing something) is seen as a sufficient action to wake up the computer, since you may be about to do something with it.
If you have a lan cable with internet access, no you do not need a modem.
An Internet working device used to connect different LAN segments is called a Modem. A Modem can be either hard wired to the computer or use a Wi-Fi connection to connect to the computer. Dial up Modems were also used that ran through telephone lines.