How to get the domain name of the page from which the link originates

1. Theoretically yes, as there has to be extra logic executed to parse the SCRIPT part. It is just really a bad practice (there still could be legit edge cases to use it this way). The code logic should be in a code file. The ASCX transformations are virtual so there is no code file = add the logic to the custom transformation method class. It is better from the debugging, maintenance and "for future developer" perspective. Using it the way you are using it, it might be difficult to find the code in the future for somebody else. Not mentioning that you will need to move to MVC development model at some point.

2. Consider switching to text transformation and use macros - no need for extra transformation methods. you could use macro like: {% CurrentDocument.NodeLinkedNode.NodeOriginalNode.Site.SiteDomainName %}

3. The code could look like this, but I would still recommend using it inside a custom transformation method (this is where I tested it):
   public partial class CMSTransformation {

       public string CustomTransformationMethod(int NodeID)
       {
           TreeProvider tree = new TreeProvider(MembershipContext.AuthenticatedUser);
           var page = tree.SelectSingleNode(NodeID);
   
           string domainName = page.Site.DomainName;
   
           return domainName; 
       }
   }
   

And then, in the ASCX transformation: <%# CustomTransformationMethod(Eval< int >("NodeLinkedNodeID")) %> (do not forget to add the NodeLinkedNodeID column name to the Columns property list so the listing web part gets the value. )