In the IPAD User Guide, there is a section titled: "Adjust the settings for connecting to a Wi-Fi network". In this section it talks about setting HTTP proxy, define network settings, turn on BootP or renew the settings provided provided by a DHCP server. What are these and should I worry about selecting them?
Wi-Fi seems to be working OK except I can't receive incoming FaceTime alerts or calls UNLESS the FaceTime screen is open.
Unless you know what they are, no there's no reason to be messing around with them. If Wifi works then all the settings have been provided correctly by the DHCP server. Which in most cases is your Wifi router, or access point. So there's no need to change them.
As for the Facetime notifications, you can go to Settings->Notifications->Facetime and make sure its set to on in the Notifcation Center. You can then configure the type of alerts and ringtone you want for it.