Decide if class has generic ancestor of specific generic argument type

Say I have a class CoolStorageClass, which inherits from StorageClassBase:

public abstract class StorageClassBase
{
//does something
}

public class CoolStorageClass : StorageClassBase
{
}

Then I have a generic abstract BaseClass<T> (which implements interface IBase<T>, which is probably not important for the question). It is important, that T can only be of type StorageClassBase.

public abstract class BaseClass<T> : IBase<T> where T : StorageClassBase
{
}

Then I have the implementation of the BaseClass with T as CoolStorageClass in the form of CoolClass:

public class CoolClass : BaseClass<CoolStorageClass>
{
}

I want to select all of my object, which are implementing the BaseClass<StorageClassBase> abstract class.

1. does it make sense to check the generic of BaseClass? I mean, I could have classes, which inherit from BaseClass<DifferentStorageClassBase>...

2. how do I check if a Type implements BaseClass<StorageClassBase>? I have found following [answer][1], but it does not check the type of the generic parameter. So I modified it into this:

   public static class TypeExtensions
   {
       //https://stackoverflow.com/a/457708
       public static bool HasBaseClassOf(this Type t, Type toCheck, Type genericParameter)
       {
           while ((t != null) && (t != typeof(object)))
           {
               var cur = t.IsGenericType ? t.GetGenericTypeDefinition() : t;
               if (toCheck == cur)
               {
                   //also check whether the generic types match
                   if (t.GenericTypeArguments[0].IsSubclassOf(genericParameter))
                   {
                       return true;
                   }
               }
               t = t.BaseType;
           }
   
           return false;
       }
   }
   

But this only checks for one generic type, and I don't understand why I have to check t.GenericTypeArguments instead of cur.GenericTypeArguments.

3. What is the correct way to check for all the generic type arguments and the BaseClass?

4. Currently I have to call the function like this: o.GetType().HasBaseClassOf(typeof(ProxyBase<>), typeof(ProxyDataPointBase)). How should I modify the function to be able to call it like this: o.GetType().HasBaseClassOf(typeof(ProxyBase<ProxyDataPointBase>))? [1]: https://stackoverflow.com/a/457708