I plan on visiting China for a week on a tourist visa to visit my son who works there.

I am a British citizen, living in Dubai, but with a residence visa in Abu Dhabi (we moved to Dubai recently from Abu Dhabi). I have two questions:
1) Do I need to apply through the Chinese embassy in Abu Dhabi or can I do through the Dubai consulate?
2) I will be travelling alone. I am a housewife and therefore not employed (my husband works). Do I still need to get a no objection letter? If so, would this be from my husband?