You can have a "bond" with your dog but you cannot have "feelings" or "feeling" with your dog. Instead, you have feelings or a feeling FOR your dog. "Feelings" and "feeling" can be used interchangeably. Say "I never imagined" rather than "I had never imagined". The past perfect is not needed. You could use past perfect this way: "Before my dog's death I had never imagined..." Use of the past perfect requires some reference point in the past. Instead of "would be stronger even", say "would become even stronger". That way "even" modifies "stronger", as it should. So, "I never imagined that the bond I had with my dog and the feelings I had for him would become even stronger after his death."

1. passed away is more typically used for human beings than for animals.

the second one. The first one would be better if you took out the word "even"