Do SSIS columns have custom properties?

The answer is yes. SSIS columns are objects that inherit the IDTSColumn130 interface. As mentioned in the SSIS documentation , this interface contains a property called CustomPropertyCollection that contains the collection of IDTSCustomProperty100 objects added to the input by the component.

Some components add some custom property to the SSIS columns such as the Derived Column Transformation. As I know, a custom component called FriendlyExpression is used to store the expression in plain text form. But, there is no way to add custom properties in the Integration Services package designer (Visual Studio).

How to add Custom Properties?

I think the only way is to create packages programmatically and edit those values or develop a custom SSIS component that adds these properties at runtime.

This is an example of reading the custom properties of a Derived Column transformation using C#. ( Reference )

foreach (IDTSInputColumn localIColumn in localInput.InputColumnCollection)
{
    if (localIColumn.CustomPropertyCollection.Count == 2)
    {
        repository.AddAttribute(componentRepositoryID, localInput.Name + " [" + localIColumn.Name + "] [ID: " + localIColumn.ID.ToString() + "]", "From [" + localIColumn.UpstreamComponentName + "] " + FormatColumnDescription(localIColumn.Name, localIColumn.DataType, localIColumn.Length, localIColumn.Precision, localIColumn.Scale) + " Expression " +
            localIColumn.CustomPropertyCollection["FriendlyExpression"].Value != null ? localIColumn.CustomPropertyCollection["FriendlyExpression"].Value.ToString() : "Not Available"
            );
    }
    else
    {
        repository.AddAttribute(componentRepositoryID, localInput.Name + " [" + localIColumn.Name + "] [ID: " + localIColumn.ID.ToString() + "]", "From [" + localIColumn.UpstreamComponentName + "] " + FormatColumnDescription(localIColumn.Name, localIColumn.DataType, localIColumn.Length, localIColumn.Precision, localIColumn.Scale) + " Expression (See Ouput Column)");
    }
    //repository.AddObject(localIColumn.Name, "", ColumnEnumerator.ObjectTypes.Column, componentRepositoryID);
}

Alternatives

You can store the columns metadata within an external data source (SQL, XML, ...) and load it at runtime. Or you can use the Description property as you mentioned in your question.

I usually add a JSON string to the comment section. You just need to set your own standard. When you do "SELECT" just always include the comments (obtainable from the schema), and then process the data on the script level by parsing the comment as a JSON object/string or whatever.