A few corretions 2

Can I say,

(a) When Peter found his lost his door keys, he decided to wait for his mother back. He sat on the steps (out of / outside the door) for a long time. He felt very bored.

(b) He decided to wait outside his home / house.He sat at the (door)steps and slept simultaneously.

(c) Peter was sad because he could not go in/ into his house. He decided to wait for his mother (to) came back home/ coming home. He sat at the stairsteps.He felt tired so he felt asleep.

(d) Peter then decided to wait for his mother. He sat on the steps and eventually fell asleep while waiting for his mother's arrival.

(e)Peter tried to open the door but he failed. Later, he decided to give up and sat outside the door. / He sat on the flock of steps quietly. Then he fell asleep.

(f) He sat on the steps and did the homework while waiting his mother. After half an hour, a woman went to his house and returned the key to him. She told him that he left the key on the bus. Peter opened the door and went it happily.

(g) He sat patiently during the waiting time.