This is what I see Enzo's favorite stuffed animal would look like. He would keep this is the first toy that Denny gave to Enzo when he was a puppy which is why when Mike tried to wash it, Enzo got upset. I think that this toy symbolizes as a way to protect Enzo from anything. Another thing that I think it could represent is a hint to Enzo that he should focus on enjoying being a dog.
Since Denny was a race car driver and Enzo loved to race like Denny did, it's only natural that Enzo would keep a racing helmet that used to be Denny's. Racing in this story is a big symbol representing life so the helmet( with other racing gear ) could represent you being prepared to live on and take on any difficulties.
Zoë could have thrown the jacket under her bed after she got upset about her toys being destroyed by "Enzo" and maybe she ends up pulling the jacket out of a box from after Denny and her moved to Italy. The jacket could represent memories of Zoë as a child like how Eve's necklace represented memories of her. She might save the jacket and give the jacket to her children if she has any.
Enzo said that his favorite food was pancakes so I would think that if Enzo had to keep something he would take pancake mix with him so he can make pancakes. He stayed that he liked pancakes and even Denny's mention that pancakes were his favorite. Enzo tried eating pancakes before he died in the end of the book.