I am trying to write a program using C# to act as a multipurpose tool for my company. One of the things we would like in this tool is to determine if IPv6 is enabled/binded
You can query for exactly what you asked for (if IPv6 is enabled or disabled for a specific network adapter) with the following code using the System.Net.NetworkInformation namespace:
using System.Net.NetworkInformation;
// ...
NetworkInterface[] allInterfaces = NetworkInterface.GetAllNetworkInterfaces();
NetworkInterface firstInterface = allInterfaces[0];
bool interfaceSupportsIPv6 = firstInterface.Supports(NetworkInterfaceComponent.IPv6);
Documentation on MSDN: Link