Since this is a Catholic apologetics forum, I’ll assume you want an answer from what the Catholic Church and its theologians teach. Propositions 1 & 2 are both legitimate expressions of Catholic faith. Let’s look at 1 first.
The Nicene-Constantinopolitan Creed in English states: “I believe in one God, the Father almighty, maker of heaven and earth, of all things visible and invisible.” In fact, it is a de fide tenet of Catholic belief from the First Vatican Council and Lateran IV that God created the universe and everything in it ex nihilo - from nothing, from no pre-existing matter or energy. A transcendent Being that is truly “almighty” or “all powerful,” from the Latin root omnipotentem It does not mean that God can do “anything,” in the broad sense of the word.
But I’m concerned. The first does NOT prove God can do anything it just proves His power is astonishing. The ability to perform miracles does not mean He can perform any miracle at all.
Proposition 2 states that with God, all things are possible. Catholics are obliged to believe this as Jesus himself said it. Matt. 19:26. However, this has never been interpreted by the Church to mean that God can engage in logically impossible states of affairs or can contradict His own divine attributes. As Aquinas wrote:
I answer that, All confess that God is omnipotent; but it seems difficult to explain in what His omnipotence precisely consists: for there may be doubt as to the precise meaning of the word ‘all’ when we say that God can do all things. If, however, we consider the matter aright, since power is said in reference to possible things, this phrase, “God can do all things,” is rightly understood to mean that God can do all things that are possible; and for this reason He is said to be omnipotent.
For example, God cannot deceive (lie), nor can he be deceived.
He cannot deny himself, nor can truth ever be in opposition to truth.
[Vatican I.](“http://www.ewtn.com/library/councils/v1.htm#4 Vatican I”)
So some “things” that God cannot do are lie, be deceived by anyone or anything, or contradict something that is true about Himself. I use the term “things” loosely because these “things” denote a lack of perfection and a lack of being. A God who could be deceived would not be almighty. A God who could lie would have the ability to impart not-truth, a lack of something. A God who could contradict his own divine attributes (not be omnipotent?!) would then lack one of the very things that make Him almighty.
Where’s the proof? His omnipotence is dogma so I expected infallible evidence not this lack of…As we English say (well, in American cartoons): blimey!
It depends on what you will accept as proof. As a Protestant, I don’t require that you accept the Catholic Church’s say so on the matter; but I can give you what it teaches.