How are two events enough for certainty that it’s not accidental? Isn’t that too little?

There is never *certainty* that something is not accidental. Even a million events could happen by chance (with a very, very, very low probability that probably wouldn’t occur in the next 100 billion years).

But still, three events combine to support the logic of Occam’s razor, and that makes sense. But to infer that from two events—isn’t that too hasty? Like the example of the imbecile, where three characteristics are combined?

As D said, there is no certainty. Clearly, the more cases there are, the greater the probability of an explanation that ties them all together. The question is where to draw the line. It could have been drawn at two cases, or three, or ten. That is a halakhic decision, not a factual one.
The example of the imbecile that you brought is actually evidence to the contrary. After all, in the Talmud it is connected to a presumption established by three occurrences, and regarding a three-time presumption the tannaim disagreed (see Yevamot 64a and many other places) whether it is after two times or three. And even in practical Jewish law there are cases ruled on the basis of two and others ruled on the basis of three (see the distinctions there in the Talmud itself).
By the way, based on this I explained that all the difficulties raised by the later authorities regarding various cases of three-time presumptions (such as in Kehillot Yaakov, Taharot, no. 47)—whether this is a sign or a cause, and how one compares a sign to a cause (such as Maharam of Rothenburg and Rabbenu Peretz regarding saying “Give dew and rain”)—are fundamentally mistaken. Sometimes it is a sign and sometimes it is a cause, and still they can be compared. The comparison is not because of probability (for probability differs in every context, even from one sign to another or from one cause to another), but because the question is where Jewish law draws the formal line. And if it is decided that it comes after three times, then that applies both in situations where it is a sign and in situations where it is a cause. And from here all the dialectical discussions of the later authorities on this matter collapse into the pit, and this is not the place to elaborate.

One more comment about the haste you mentioned. That is simply a mistake. Suppose the line is drawn after three times, as you suggest. Now you see an ox that has gored twice. You would not say that it is forewarned. Isn’t that also hasty? You have two cases against you, and still you insist? Any decision made in such a situation can be considered hasty—whether the line is drawn after three times or after two.

If I understood correctly—there is no connection between Jewish law and ordinary matters. And regarding combining the phenomena that make the Jewish people unique, which are ordinary matters, there is a preference for one overall explanation of three or two, depending on the case, rather than separating them. But it isn’t necessary; it isn’t factual.
Is the conclusion that there is a cause for the uniqueness of the Jewish people, in light of the many unique phenomena, not too fateful a conclusion given the understanding that it isn’t factual?

Why is there no connection? There definitely is.
I couldn’t connect even two words of the rest of your message.

Combining the claims about the uniqueness of the Jewish people creates a strong claim, and it makes more sense to argue that claim than to separate the claims—according to Occam’s razor. And despite the combination, it still isn’t certain, only more reasonable.
Is it right to base faith / belief (a significant decision) on common sense, when it is not necessarily correct? After all, there is still a chance that everything is accidental.

There is nothing in the world that is certain. The fact that an airplane works is based on scientific generalizations, and yet we board airplanes. The same is true of cars and elevators and medicines and the rest.
As human beings, we have no escape from uncertainty in anything we think about. Someone who seeks certainty will not be able to accept any claim. The question of what level of solidity is required is a question with no clear answer, and each person will have to answer to himself.