You set a password off the settings of your router
A Mac's airport card connects the Mac to a wireless network. If the Mac is turned off it will not be connected to the network.
Yes, by its mac address.
Unsecured wireless network without MAC filter.
MAC filtering
The Xbox 360 Wireless adapter uses standard 802.11b, 802.11g, and 802.11a connections. If your Mac has an AirPort wireless network card it will be able to connect to the Xbox network.
Use security settings for your wireless network, such as SSID hiding, and wireless encryption. It's better if you use WPA AES at least, but WPA-PSK2 AES is better. You can use also MAC filter. But if you have WPA-PSK2 AES you do not need to because it's almost impossible to crack the encryption.
Once you have your WiFi network up and running, give the network a name, just turn on your Mac and then click System Preferences > Network and turn the WiFi on. Your Mac will pretty much do the rest and will connect the the network.
As long as the Mac in question has a wireless adapter, it should connect.
A person may find instructions on how to setup a secure wireless network using a MAC address filter online. Some websites that offer these instructions include About and Instructables.
If a hotel has a wireless network that they allow their customers to use then you can take a Mac Mini and use it.
A Dell router using standard settings will work with a Mac. If there is a wireless network already established then the Mac should be able to connect to that.
MAC address filter is a pretty secure way of rudimentary network security. Enabling it makes the network available only to know devices. However, this leaves it vulnerable to MAC address spoofing.