I tried google image and slim coat seem to me like what I understand as a "wąski płaszcz".
I'm not sure, but I think that would simply mean that the coat is too tight for you, ergo it's too small.
Nope. Tight can just mean that it fits close to the skin, not that it's too small. Narrow coat is not idiomatic.
in English coats are never called narrow. This is a silly sentence. It might be a 'slim- line coat but not narrow.
i guess, it is better to say tight in that case. the thing is that in slavic languages we use mostly one word for describing tight clothes and a narrow channel or passageway for example. they are "узкий" (russian), "вузький" (ukrainian) and wąski in polish. i'm not 100% sure about polish, cause i only started learning it. i hope this will help you understand the difference.
Nobody in English uses narrow in regards to clothes. It should be tight instead