Translation:This is fish, but I do not eat soup with fish.
Yes, the default meaning of "X with Y" in food is "Y X" in English :D E.g. Суп з рибою = fish soup, салат з помідорами = tomato salad.
In some cases it's possible to say "Y (adjective) X" instead of "X with Y" e.g. рибний суп = суп з рибою. Sometimes there's a slight difference e.g. грибний суп = mushroom soup, суп з грибами = soup that has mushrooms in it (but maybe it's a fish soup, just also with mushrooms).
It's very seldom that "X with Y" means separate things, e.g. soup and fish, not fish soup. As far as I know nobody says "X with Y" in that case, they would say "X and Y".
In case X and Y are not "mixable" (it's not a soup or a salad etc.), then "X with Y" just means "X and Y" e.g. Я їм рибу з помідорами = I'm eating fish with tomatoes, not a dish, just eating fish and tomatoes.
Yes, this is correct!
You can find tips like these in every lesson though, if you don't want to be guessing all the time:
You click on the "ball" first and then on the lamp symbol, and this will pop up.
F: Це риба. (This is fish). Ця риба (this fish)
M: Це кіт. (This is a cat). Цей кіт (this cat)
N: Це молоко. (This is milk). Це молоко (this milk) <-- THE TRICKY BIT
You are partly right :) It still works with "fish" in this case, but they do clash with neuter.
'This is fish' is «це риба», here це is an noun-like pronoun that doesn't change its form.
'This fish' is «ця риба», here ця is an adjective-like pronoun that changes its form according to the form of the noun it modifies (here it has a feminine form, ця, because ри́ба is feminine). Masculine form is 'цей', neuter is 'це'.
The confusion can arise only with neuter nouns: це ві́кно can mean either 'this window' or 'this is window'. With neuter nouns, you can distinguish the two meanings only be context and by intonation.