The 'a' is not necessary in this sentence
'Coffee with milk and sugar'
'A cup of coffee'
"Coffee with milk and sugar" is an accepted translation.
Another example for the Polish language making it more complicated than necessary: 'cukier' loses its 'i' in the instrumental case while for 'mleko' an 'i' must be added :D
It's called a "regular coffee" in NYC.
I hear 'z mlekim' instead of 'z mlekiem' (female voice). How should it be actually pronounced?
There is definitely something wrong with the female audio here.
The IPA is /mlɛkʲɛm/