I don't get your qustion right maybe. Every router can do wifi to connect your computer with it, but you need a special router (or software on the router) to connect up to your ISP, and that depends on whether you are connected via landline phone (copper line), glass fiber, or cable tv.
There are two caveats I always heeded, and fared well so far:
1) Do NOT EVER be dependent on one company. Have a landline phone with your DSL line at a different company than your cable tv provider is connected with, and if possible, have a mobile phone at yet another provider. And check before you sign that the three aren't just different brand names of one company. Having a backup option in an emergency is just priceless.
2) Do NOT buy Netgear stuff. There have been so many security leaks detected in their cheaper routers in 2016, I can't trust them anymore, especially in tjose provided by cable companies worldwide. I live in Europe, and I keep using AVM routers (Fritz!Box), and recommend them to everyone. They come at a price, of course, but they're worth every euro.
Assuming the NetGear router you are using has wifi and it is active, this allows a wifi-capable network element (like a computer) to connect to the router wirelessly.
The router also connects to a modem and the Internet Service Provider's connection with a wire (whether cable modem, DSL, fiber-optic connection).
No. As long as the netgear router has a wireless capability, then it will give you an option of having a wifi network.
Of course, that wii network might not connect to anything like the Internet! To connect to the Internet you need cable or broadband or some similar connection capability.
Providing it is a wireless router and has power, it can be used to establish a WiFi network. This network can allow suitable wireless (WiFi) devices to communicate with each other. For example, one could be a media server and another could be a media player playing music or movies stored on the media server.
It won't provide Internet access.
No cable and wifi are to completely separate things. Wifi is a means to connect to a network. You do not need cable or internet to connect to a network. Assuming that you actually mean cable internet when you say cable. I will say that you do need internet to access the internet. Whether or not you use wifi to connect to that internet is a different question.
No. Netgear make a range of routers for all types of connections.
Who is your provider? Asus routers are more reliable and more powerful