No, Amanda is not an orphan but she wants to alone in peace. Saying so, she gives example of an orphan who has the freedom to enjoy making patterns on soft dust with his bare feet. She is so distressed by the unceasing instructions that she yearns for some silence and peace.  

The girl yearns for a life full of freedom. Amanda represents many children of her age who are victims of the too much control of their parents. Such children tend to live their freedoms in their thoughts. As they are too much dominated to speak their thoughts, they resort to loneliness to stay peaceful.

Rapunzel was a princess who was held as a captive by an enchantress in a huge tower. She had beautiful and very long hair. The tower where she stayed had a little gate that too at a great height. When the enchantress would come back, she would ask Rapunzel to throw her hair down so that she could climb up the hair to get into the tower. 
Amanda wants to be a Rapunzel because wants to enjoy the freedom that Rapunzel enjoyed in calmness inside the tower. She also says that she would never let her bright her down to help somebody get in the tower and dominate her.

The speaker in Stanzas 2, 4 and 6 is the little girl, Amanda. And, the speaker in Stanzas 1, 3, 5 and 7 is her parents. No, Amanda is not listening to her parents; She is responding to their instructions in her thoughts. This is because she wants a way of life in which she can enjoy freedom.