"across the room from the entrance of the house" or "looking toward the entrance to the house"
# she received approval in his eyes
The word "eyes" refers to his sight and is a metaphor for his evaluation of her. This can be stated in active form. AT: "he was pleased with her" or "he approved of her" (See: [[rc://en/ta/man/translate/figs-metaphor]] and [[rc://en/ta/man/translate/figs-activepassive]])
# He held out to her the golden scepter in his hand
He did this to show that he he was pleased with her.
# touched the tip of the scepter
She probably did this to to show that she respected his authority and was thankful for his kindness to her.