All is described in the Scripture concerning this or deduced in my post. For the restoration of creation and it's freedom from death in general in the Kingdom:
"I consider that the sufferings of the present time are not worthy to be compared with the glory that is about to be revealed to us. For the eagerly expecting creation awaits eagerly the revelation of the sons of God. For the creation has been subjected to futility, not willingly, but because of the one who subjected it, in hope that the creation itself also will be set free from its servility to decay, into the glorious freedom of the children of God. For we know that the whole creation groans together and suffers agony together until now. Not only this, but we ourselves also, having the first fruits of the Spirit, even we ourselves groan within ourselves while we await eagerly our adoption, the redemption of our body." (Romans 8)
This passage speaks of how when the sons of God are glorified all of creation will enter into their freedom and be set from from decay (death, corruptions, etc). The animals are included in this, for in the Fall of the first Adam death entered into the cosmos and discord between the animals and us, so in the Resurrection of the last Adam (Jesus Christ) this is reversed. This is where the recapitulation of animals is put in, for also St. Paul said in Ephesians: "for [in] the administration of the fullness of times, to bring together all things in Christ, the things in the heavens and the things on the earth." And so the recapitulation of the kosmos (where animals and their spirits are part of) is placed in. St. Paul also said that we are made new in the image of the one who created us, which is again speaking of how the last will be like the first and vice-versa, but after the first creation in the image and likeness (and those in Christ are the new creation in the image and likeness) what was said to man? "Have dominion over the fish of the seas and flying creatures of heaven, and all the cattle and all the earth, and all the reptiles that creep on the earth." And so this will also be in the future as well, in a deathless way.
Due to this kind of reading the Scriptures is why there is the idea of a restoration of all things, and creation to be in a deathless state as it was made, because we are and all things are, being remade in Christ, soul and body, Heavenly and Earthly.
For Heaven and Earth being united, God was in the Garden of Eden and so in the end "behold, the dwelling place of God is with man. He will dwell with them, and they will be his people, and God himself will be with them as their God." There was no death there and likewise after this verse from Revelation it says "there will be no more death or mourning or crying or pain, for the former things have passed away." So this union and dwelling is unique.
The spirits being visible is due to "we shall judge angels" (1 Cor 6:3) (in that age), and the spiritually dominated bodies we'll receive as spoken of in 1 Cor 15, and also there are accounts in the Scriptures of when God allows a person to see through that sort of sight they see the spirits with their eyes, so also it will be then.
All in my opinion at least.
