"My cheese sandwich is in the fridge."
Translation:Mi sándwich de queso está en la nevera.
No, "refrigerador" is masculine and must be used with "el". It is not a noun that changes genders. Most nouns do not change genders (whereas, adjectives do). The exception are nouns that tell you someone's occupation and some animals change based on the gender of the animal.
Apparently it's "la refrigeradora" in Peru
Duo may forgive you if you leave out the diacritic in sándwich but will fault your answer if you write esta instead of está. It may let your misspelling of nevera pass, but it's a good idea to use the correct spelling.
As for your queso sandwich, some online translators might translate that as 'cheese sandwich', but remember that adjectives in Spanish don't precede the noun but follow it.
I hope this helps.