At first sight, it does appear that there is a logical contradiction in saying that God is both infinite in power, creativity etc. and at the same time claiming that God is limited by being loving, good and pure. However, a more precise understanding of what we mean by the "Omni-s" leads to the conclusion that there is no such contradiction.
First, it is worth establishing that something can be both infinite and limited at the same time.
For example, consider normal counting numbers - 1,2,3...etc. These are known as integers. Mathematicians tell us that, logically, there are an infinite number of integers. However, we also understand that integers have limitations. That you can't represent 1.5 using them, for example. They are unlimited in that there is an unending sequence of these numbers.
Secondly, we'll use analogy to help us understand the kind of limitations we might be talking about. Hopefully, this will help us understand what kind of question we're considering.
Imagine a torch with a nice bright beam. Obviously, you can use that torch to illuminate things that are in darkness you can observe them. Someone might claim that you can use that everything illuminated with that torch can be seen better. And this is a perfectly legitimate claim. It appears that the torch can illuminate an infinite number of things that are in darkness to make them visible. However, someone else might claim that, if you shine your torch on darkness (on a shadow, say) then that darkness becomes less visible. Therefore the torch is limited. How can a torch be both infinite in its capacity to illuminate and at the same time be limited in that it can't illuminate things like shadows?
Next, we will establish that a more precise definition of the 'Omni-s', and look at what these definitions imply about God's limitations.
When we say that God is Omniscient (all-knowing), we understand that he knows everything that is true or could possibly be true. However, there are some things that God cannot know. For example, He cannot know something that isn't true. For example, God cannot know that 1+1=4 as that simply isn't the case. In that sense, God's Omniscience is limited.
When we say that God is Omnipresent (present everywhere), we understand that God is everywhere throughout all time. Does this mean that God is present in places that don't exist? Presumably not. Does it mean that God can remain Omnipresent and at the same time choose not to be present in, say, my kitchen? It does indeed (which is not to say that He has to make his presence known - he has to be present, but that doesn't mean we have to be aware of Him). In the sense that it would make no sense to speak of God as both present and not-present, God is limited.
When we say that God is Omnificent, we are saying that He is unlimited in creative power. He can create anything that can be created. Does this mean that He can create something impossible like a square circle or an eternal thing that ceases to be? Presumably not (although some philosophers have attempted to remove this limitation by suggesting that God could remove the laws of mathematics and logic. Even if this is possible, however, we see that God is limited in the sense that He can't achieve these things without this kind of drastic re-engineering of reality).
Finally, the most debated and controversial of the "Omni-s": God's Omnipotence. When we use this term, we mean that God can do anything that can possibly be done. We don't, however, mean that God can stop being God and remain Omnipotent. A classic question is whether God can create a rock so heavy that he cannot lift it. There are various possible approaches to answering this. You could say "yes", but that he chooses not to. Or you could say "no", otherwise He would cease to be God. Or you could say, "yes" but the laws of logic would need to change. Each of these solutions implies some kind of limitation on God. We might argue that these apparent limitations are either self-imposed by God, or that they are necessary in the sense that God cannot be simultaneously God and not-God. Nevertheless, there is some kind of limitation here. It is worth noting, however, that no other entity in the Universe can overcome these limitations either, so God still retains His place as supreme being despite these logical necessities.
In conclusion, we'll examine the claim that God's Omni-s are incompatible with the characteristics ascribed to Him by Christians.
Most importantly, Christianity don't necessarily claim that God is unlimited. On the contrary, many of us understand God to be intrinsically limited. For example, we believe that God cannot be:
However, the fact that God cannot do certain things doesn't invalidate the claim that God is characterised by the various "Omni-s", it just clarifies what we mean by them. Nor does it make God anything but God.
Considering some of the characteristics of God that you mentioned:
Love: When the Bible says that "God is love", this doesn't imply that God is only love. Indeed, most Christians would say that God is also justice, for example. The important point here is that "God is love" doesn't imply that God can't hate. He loves us, certainly, with a love beyond measure. However, this in itself implies that he hates injustice, cruelty and other evils because not to do so would be unloving towards human beings. (The reason Christians often emphasise love is because we're interested in how God feels about us, not because love and hate are mutually exclusive). Love provides no challenge to God's omnipotence.
Goodness: Certainly, we believe that God cannot be evil. It would appear, then, that we humans can be something that God can't. However, it is reasonable to think of evil as an absence of goodness. From this perspective, for God to become evil he would have to limit his ability to be good. Therefore, His omnipotence would be reduced by his being evil rather than being enhanced by it. Furthermore, you could argue that whilst God cannot be evil (because that is against his nature), he certainly has power over evil, and in that sense he remains omnipotent.
Purity: When we talk about purity, we mean that God cannot be not-God. He must be completely true to Himself in all ways and at all times. Again, this doesn't limit his omnipotence any more than in the ways we've already discussed.
It is perfectly valid, then, to accept that God has certain characteristics - love, purity, goodness - whilst maintaining that God is Omnipotent etc. Indeed, it is arguable that these are freedoms rather than limitations.
Finally, I do want to address some of the minor misconceptions in the question.
First, your assertion that Schrödinger's cat is dead or alive but not both is in direct contradiction to the most commonly held interpretation of quantum mechanics, the so-called Copenhagen interpretation, which states that the cat is indeed both dead and alive until you look in the box.
Secondly, Christians don't typically make claims about what God looks like. (True, he wrapped himself in a human body to pay his creation a visit, and we can say something about the appearance of his "flesh suit". However, that says no more about God's appearance than my telling you that I sometimes wear a blue jumper tells you about the appearance of my kidneys).
Finally, you said that "only God understands how this can be" is not a valid answer. However, whenever we talk about the infinite we must contend with the fact that our minds are finite. We cannot possibly develop a complete answer to the kinds of questions you're asking. I appreciate that this is intellectually unsatisfying. Moreover, I would agree that recognising that our task is impossible is no excuse for providing no answer whatsoever. Nevertheless, when it comes to discussing God's limitations, we must first recognise our limitations. We may never be able to satisfy our longing for a full and complete answer in this area.
(What God demands of us, however, is that we live by the light we have received, and respond to Him in on the basis of the things we do understand about Him, regardless of how limited that understanding might be.)