Step 1) A partial view is part of a page. So if you create a doctype with _Layout = null; and the partial call in it, you can display only the partial.

Step 2) Create a Node of the doctype you just created. Now you can link to this node

Step 4) Create some display code to example that uses our.umbraco.corepropertyvalueconverters package below

var links = Model.Content.GetPropertyValue<RelatedLinks>("relatedLinks");

foreach (var link in links)
{
    if (link.IsInternal && link.Id.HasValue)
    {
        var linkedItem = Umbraco.TypedContent(link.Id.Value);
        if (linkedItem.DocumentTypeAlias == "docTypeAliasOfyourPopupDoctype")
        {
            // render it as a popup
        }
    }
    else
    {
        // render it like normal
    }
}