How to make fields of a cloned node available in Rules
The problem was that I had to fetch the entity by property [cloned-node:author:field-firstname] inside the conditional and set the data value [cloned-node:field-student-name:0] to [firstname-fetched:0:field-firstname]
I still don't understand the actual logic why [firstname-fetched:] has to be followed by [0:field-firstname] but that works. See screenshots. 
Hope this helps someone else out too. 








After @Pierre.Vriens helped out my component code is now: 

    { "rules_update_the_cloned_course_with_values_for_the_student" : {
    "LABEL" : "Update the cloned Course with values for the Student",
    "PLUGIN" : "action set",
    "OWNER" : "rules",
    "TAGS" : [ "cloned node", "component", "course", "update" ],
    "REQUIRES" : [ "rules_conditional", "rules" ],
    "USES VARIABLES" : {
      "node_to_update" : { "label" : "Node to be updated", "type" : "node" },
      "node_author" : { "label" : "Node author", "type" : "user" }
    },
    "ACTION SET" : [
      { "CONDITIONAL" : [
          {
            "IF" : { "entity_is_of_bundle" : {
                "entity" : [ "node-to-update" ],
                "type" : "node",
                "bundle" : { "value" : { "course" : "course" } }
              }
            },
            "DO" : [
              { "data_set" : {
                  "data" : [ "node-to-update:field-student-name:0" ],
                  "value" : [ "node-author:field-firstname" ]
                }
              },
              { "drupal_message" : { "message" : "Machine name of this Component was: \u0022rules_update_the_cloned_course_with_values_for_the_student\u0022" } },
              { "data_set" : { "data" : [ "node-to-update:field-status" ], "value" : "359" } }
            ]
          },
          { "ELSE" : [
              { "drupal_message" : {
                  "message" : "The field \u0022Student name\u0022 could not be set with the value of the Student\u0027s first name.\u003Cbr \/\u003E\r\nMachine name of this Component was: \u0022rules_update_the_cloned_course_with_values_for_the_student\u0022",
                  "type" : "warning"
                }
              }
            ]
          }
        ]
      }
    ]
  }
}