Chef has a positive connotation because the term "Chef" is usually used to describe a person who has undergone culinary school and works in an upscale restaurant or as a private chef. A cook is typically seen as a lower skilled chef and therefore has a negative connotation.
This is a good reference:
https://www.reluctantgourmet.com/difference-cook-chef/
Living is the correct adjective
It'd help if you'd provide the sentence.
Answer: Change there to their.
Answer:
wht's the question in this ?
Explanation: