"I like eating noodles with chicken."
I'm confused about why the word "chicken" has to go before the word for "noodles"?
It is correct as it is, because "面条和鸡肉" sounds like two different dishes or ingredients. Here you would like one dish, a combination of noodles and chicken. In the Chinese logic the distinctive part comes at the front, and the main part (that is the basis for many dishes e.g. rice, noodles etc.) follows.
The Chinese sentence actually refers to a dish where chicken is placed on top of noodles.
The sentence strucuture seems to be upside down like many are ....it a crapshoot . The sentence clearly had noodles following eating not chicken...
Ambiguous statement. Do you like to have noodles when you eat chicken? (I like eating mixed vegetables with fish). Do you like eating noodles with chicken mixed in?
我喜欢吃鸡肉面条 is more lile "I like eating the chicken and noodle dish" It's implied that we know which chicken and noodle dish... this is like what you'd say to somebody who goes to the same restaurant as you.
Yes. It clarifies that you are eating the meat part, as opposed to chicken feet (鸡爪) or some other part.