OP, let me take a slightly different approach. The answers above are good and definitely Catholic. Let’s add another dimension. You are right to point out the vastness of Creation, but remember that we know very little of it - this tiny planet called Earth. What we do not know (yet) is how much He loves the rest of the Universe.
We can only speak to our gifts - the gift of Creation, of fellowship to the Lord, of authority and dominion over the Earth and all that lives in it, and of forgiveness, mercy, and Grace. The most precious gift of Jesus Christ, His Ministry, His Church, His Sacrifice upon the Cross and His Victory over Satan. The promise of Jesus Christ to those who love Him, Eternal Life with the Lord and the companionship of the Holy Spirit to deliver us there.
But we know almost nothing of what our Lord God gave the rest of the Universe. We therefore cannot speak to our being uniquely special, but rather special in a unique way. To put it another way, a father loves each of his children uniquely, according to who they are and what they need. He may love a daughter in a different way from a son, or a younger child differently from an elder, but there is no question of his love being special for all of them, and unique to each without being less special. Likewise, Our Father loves us in a special and unique way, not because of anything we have done, but because of He who created us, and He loves all His Creation in the way that He is and the way that He chooses to.
So that said, I think it won’t help to understand God’s actions by saying “Here’s this Universe, why are humans singled out for being so special”, but rather we should ask “What is it about God that makes Him so giving towards us?”
We know from Scripture that Jesus Christ is loved most of all by God and occupies the place of most importance (Matt 28:18). Because the Lord Jesus Christ shared in our humanity, we share in his divinity, and humans are adopted children of the Living God. So humans have the first place in receiving the Love of the Father, then angels and animals (Heb 1:5,13, Rom 8:17, Gen 1:26-28). I think viewing it as a hierarchy may not be helpful because a hierarchy implies a certain consistency between objects on the same level and a sense of ownership of objects from the lower level to those above, and I don’t see those relationships being consistent between, say a hierarchy of responsibility and a hierarchy of salvation. For example, if we ask “who is responsible for whom?” we can answer that angels take care of humans and humans take care of animals. But in the hierarchy of salvation, humans rely upon God, and animals have no possibility of salvation (nor of damnation, because they don’t have souls).
No, because only humans have the capacity to be redeemed. Animals do not have immortal souls, and do not have the ability to commit sin, so no redemption is necessary. It is thought (and I’d have to dig up citations) that angels have the same kind of soul as humans (ie, different from animals) but that they do not have the ability to be redeemed - rejection of God (which is what sin is) results in expulsion from Heaven.
If I think of something has being important, I think of it in terms of mattering for some purpose. A hammer is important for driving nails and matrix algebra important for calculating eigenvalues, but I cannot compare them in terms of importance outside of their tasks - ie, neither will help me read a text in Spanish.
If I think of how God views a being as being important, it’s with respect to what that being means in the order of Creation. Plants are important for feeding animals, animals for providing for humans (arguably, before the Fall, Adam and Eve were vegetarians and did not actually eat the animals because there was no death), humans for worshipping the Lord and keeping fellowship with Him. So as I said above, God loves all His Creation in different ways unique according to the Created being.
I suppose in the same way that it’s not unjust that I didn’t teach my dog to drive or send her to college when she turned 3. I’m sorry if that comes off as silly; I don’t see any disfavor being given to other species. Why was Jesus offered for the sins of humanity, but not of cows or beetles or monkfish? Because only humans can sin. Why did God make humans in His Image and likeness but not rabbits or Yersinia Pestis? Because He desired to. Why does God offer eternal fellowship to Man but not to ferrets? He created us uniquely with the intent of being able to experience that fellowship, though I wouldn’t argue that He doesn’t take delight in ferrets. God made ferrets to be playful, cows to moo, beetles to tick and monkfish to … umm… er… do whatever monkfish do. Cows may be perfectly happy being cows, and I actually doubt they have the capacity to know what they’re missing by not being human, and I’ve met dogs who are more people-like than some humans.
There’s certainly not a balance but I wouldn’t call that unfair; this is one of those times when things are as they are for the reason that they don’t exist otherwise.