You are welcome:
so you can say "chicken with noodles" if you are eating or having chicken and noodles together.
or "chicken noodle soup", "a noodle pie" if you make a pie full of noodles.
it's noodles if the noddles are on a plate of food. or in a bowl of food but separate.
and "noodle" + the noun soup, pie etc.
There once was a craze to have strange flavoured ice cream in cones, in the UK.
If somebody invented chicken noodle flavoured ice cream. You would order a "chicken noodle ice cream"
I am not sure if Americans remove the French "our" from the word "flavour" like they do with most other French originated words, to spell it "flavor"
"chicken noodles" if you are eating or going to have a plate or bowl of noodles. Whether garnished or not or with salad or any other extras.
"chicken noodle soup" if you are having chicken soup with noodles in the soup or chicken flavoured noodle soup.