Please help me with the following question:

Question 1

On 1 Jan 2020, a well-known YouTuber, Kate, announced that she would sell her handmade jewellery Sweetie and posted a message on the social networking website called Facelook. She also placed the following advertisement in the South China Afternoon Post:

Hi, folks, I will sell my handmade jewellery Sweetie to you for $10,000. Cash on collection in my office. I will leave this offer open until 5 Jan 2020. Send me the private message in my Facelook message box.

Once after the post was shown in her fan page, she received many responses. Most of her followers were interested in buying her handmade jewellery. Kate could spot Emmas message which was posted on 2 Jan 2020. She posted the message: The jewellery looks so nice. Any other colour available? Can you accept $9,000. Kate just replied with smiling face emoji.

On 1 Jan 2020, Kates follower, Cherry, was also interested in Sweetie and asked if she could collect it in her office on 5 Jan 2020. Kate replied Yes.

On 2 Jan 2020, Kates follower, William, sent the private message to Kate and asked her whether she would accept $9,500 for her jewellery Sweetie. Kate refused and replied that she would accept $9,888 for Sweetie if he could confirm acceptance by posted letter.

On 3 Jan 2020, Emma really wished to have Kates jewellery. She found there are many messages in Kates fan page. To ensure that she could buy her handmade jewellery, she sent a letter to Kates office on the same date. Emma posted a letter to Kate and showed her sincerity by writing I agree to pay $11,000 for your jewellery Sweetie. I will collect it in your office on 8 Jan 2020. Unfortunately, Kate did not receive her letter because Emma made a mistake in the address stated on the envelope.

On 4 Jan 2020, William sent the private message to Kate I will collect it on 5 Jan 2020. Can I pay the price in 2 instalments?. Kate ignored his message and presumed that William might reject her offer if she would reply No. On the same day, William confirmed his acceptance by posted letter before the deadline for acceptance had passed.

On 5 Jan 2020, Cherry came to Kates office and found that her office was closed on 5 Jan 2020. She sent the private message to Kate who told her to come to her office on 6 Jan. As instructed, Cherry came to Kates office on 6 Jan but was told that the price was $20,000 because Sweetie became very unique and popular.

On 8 Jan 2020, Emma sent the private message to ask Kate whether she received her letter or not. Kate said that she had never received her letter and Sweetie had been sold to another follower, Harry. Emma was very angry and could not accept that Kate sold Sweetie to other buyer without the actual communication.

On 9 Jan 2020, William asked Kate whether she received his letter or not. She said that the receipt of his letter was not important because she had sold Sweetie to another follower, Harry.

Required:

(a) Advise Cherry as to whether Kate is under a contractual duty to sell the jewellery Sweetie for $10,000.

(b) Explain whether Williams posted letter of acceptance is valid in contract law.

(c) Would your answer be different if William confirms the acceptance by email at Kates request? Explain your answer.

(d) Advise whether an agreement has been reached between Kate and Emma for the sale of Sweetie. Use case law and ordinance to support your answers.