(2) What sort of wireless router to buy?
You need to get one that is for a cable modem such as you have with NTL, rather than an ADSL modem / router. I recommend that you combine the wireless router with a firewall - I use a NetGear device.
(3) I am told that NTL don't like sharing on their residential lines in case customers get ideas about setting up internet caffs, so they "do things" to make it difficult.
There really is no impediment to connecting a home network to the cable modem. I'm using Telewest and have no problems.
With Cable broadband, you will generally have a MAC address registered with the IP address assigned by your ISP. This will be the Hardware MAC address of your PC Network Card (NIC) - which could be an Ethernet-USB device or plain Ethernet.
Using a router, you need to either assign the router the same MAC address as your NIC (easiest solution) or register an alternate MAC address (the hardware MAC address of the router) with your ISP.
SD