Z application and accompanying Z for US citizen

Condition: I am a US citizen staying in Hangzhou. I need to apply for a Z for myself, and an accompanying Z for my wife. My wife is in the US and I am in Shanghai with business F.

Q1: Could I apply for the Z in Hong Kong while I am visiting Hong Kong? In person application.

Q2: Could I apply for the Z in the US, while I am in Hangzhou? For example, mail my passport to New York, and ask the agent in New York to apply for the Z, while I am conducting business in Shanghai.

Q3: Could I apply for the Z at the same time applying for the accompany Z for my wife?