Joseph - After 60 years of dreaming, exploring mine and many other people's dreams, I see that dreams are meticulously careful about what they present. Also every image or scene is to represent something other than the obvious.
So the back of your childhood house is full of meaning. It usually represents the less publicly viewed and private area of your life. Where one can be more of oneself out of the public eye, or even keep it hidden.
Also it was your childhood house, Which often refers to feelings or incidents. sometimes traumatic, that occurred in your childhood years. Remember that a house nearly always refers to you, depicting your body and aspects of your personality. This becomes obvious if, having visited friend’s houses you judge their character by the condition of the house. See
https://dreamhawk.com/dream-encyclopedia/childrens-traumatic-fears/Grilled cat - this may refer to the fact that humans have more than their human brain and have a separate reptile and mammal brain. See
https://dreamhawk.com/dream-encyclopedia/brain-levels-and-dreamBut the cat is a mammal and can represent the mammal instinctive side if you, The functions of the Mammalian brain that exist within the Human ‘brain’, MacLean likened to the skills shown in mammals such as wild dogs and apes. Mammals show enormous awareness of bonding, caring for young, group activity, hierarchy and recognition of family and pack. This part of your human ‘brain’ integrates and refines the functions of the reptilian brain. It provides emotional range and intensity, and gives a greater complexity to what motivates or deters us. It is this greater awareness of how we relate to others, and the social structure in which we exist, along with a sense of what place in it we occupy, that enables us to modify and coordinate the impulses arising from the reptilian brain.
But of course it depends on what feelings you have about cats that decides what it means in your dream. Because it refers to your childhood I can't see it relating to feelings you been having towards a friend, unless it is a trauma you experienced, which could be likely, because everything in your dream is about you - even the cat, and they were burnt suggesting great pain that you wanted to put and end to.
Dreams try to present to us old painful memories, and childhood pain when faced by adults makes them repress such pain. If you want explore yourself you could use these -
https://dreamhawk.com/dream-dictionary/getting-at-your-dreams-meaning/ and
https://dreamhawk.com/dream-encyclopedia/peer-dream-work/