I was the first person to downvote. Not because I don't grasp, but because I believe your explanation is in the best too brief to be generally intelligible. My negative opinion can be, of course, due to my stupidity, but as for my downvoting strategy, my own judgment is all I can rely upon. (My judgment also tells me that you appear a bit oversensitive to downvoting.)

Good enough for me. The sensitivity is merely a measure of my newness to LW. But, again, the sensitivity wasn't unwarranted granted your complete lack of explanation for the objection "I don't follow".

I don't see how it is relevant. Quantum branching doesn't require Omniverse. That alone makes your argument seemingly irrelevant. But let's proceed.

No, it doesn't. The question posted by the OP implied the relevance of MWI of QM. Note, in order for QM to hold any relevance to us, it must be interpreted in some way. Yes, let's proceed.

I have no clear idea what a probability of event happening in the Omniverse means.

You obviously aren't familiar with the concept (for which I cannot be held accountable). In any event, I'll explain it briefly: the omniverse is that state of affairs in which all possibilities are realized. Hence, that any event should obtain therein is an absolute certainty.

Is this supposed to justify the previous claim, i.e. that the probability of any event in Omniverse is 1? If so, I don't regard "each universe contains something, therefore any event has probability 1 in the Omniverse" a valid inference, whatever interpretation of both the premise and the conclusion I can imagine.

No, not particularly. However, even if it were so, consider this: tell me of a universe in which nothing exists. Does it make sense to posit something of which there is nothing? Equivalently: There isn't anything of the universe. But there is a thing, namely, the universe.

What is "long run"? Does it mean "in other universes" (that would make sense, but the choice of words "long run" to denote that seems bizarre) or does it mean "sometimes later in this universe" (that would be the natural interpretation of "long run", but then the statement says "p(the event happens) = 0 and the event can happen", which is a contradiction).

This is the standard understanding of what objective probability teaches: given any universe you please, a given probability of an event is supposed to hold for a particular situation in the case that one were to observe all cases (for all time). Thus, the "long run" considers a particular situation for all time. If you flip a coin, you will not observe an outcome of 50% heads and 50% tails, but were you to flip this coin for eternity, the net result is just such an outcome.

And of all that, how does anything imply, or even relate to, the "uncountably many" answer you gave at the beginning?

I'm not sure how you'd pose this question seriously. For one, the MWI and nature of QM decoherence shows a state of information as unrelated instances of a general state of things (in a coherent superposition). That there are uncountably many universes (as inhabited by any observer you please) in which the cat is alive, and so too for the cat being dead. The "cat" could even be an infinite variety of other objects, for all we damn well know.

I even don't understand what do you mean by "taking the universe as a QM event".

Then you obviously aren't familiar with MWI. Even Penrose and Hawking agree that QM applied to the universe implies MWI.

From the single sentence the OP consists of, could you quote the section where it very clearly asks for non-standard instances of the (which?) question?

Are you being obtuse to justify your down-vote or something? This is ridiculous. Now I have to justify my answer to the OP to you? Absurd. But I'll play along, quoting OP:

...what about non-50/50 scenarios...

I think that the universe is a "non-50/50 scenario", but I guess you can make the case it isn't.