Translation:My refrigerator is in the kitchen.
Why not у кухні? Is this just an exception?
same as на балконі. I guess it is an exception. At least I do not recall any rules related to this.
I think кухні also means food/cuisine?
In nominative it's кухня and yes, it does also mean "cuisine"
My fridge is in the closet.
The short for Холодильник doesn't exist?
If it does, it is not widespread,
Absolutely. Thank you for your reply!
холодно means cold. This word for fridge basically means cold box. Льоду is ice so the polish word lodówka works better in that regard. For me to renember the words anyway.