A recurring case

How are two events enough for the certainty of no coincidence, isn't that too few?

There is never a *certainty* of no coincidence. Even a million events can (with a very, very, very low chance that probably won't happen in the next 100 billion years) happen by accident.

But still, three events add up to understanding the razor principle, and that makes sense. But isn't drawing this conclusion about two events reckless? Like the example of the fool, in which three characteristics add up?

As D said, there is no certainty. It is clear that as the number of cases increases, the probability of an explanation that accounts for all of them increases. The question is where to draw the line. It could have been drawn in two cases or in three or in ten. This is a halachic decision, not a factual one.
The example of the fool you brought is evidence to the contrary. After all, it is connected in the Gemara to the assumption of three times, and regarding the assumption of three times, the Tannaim were divided (see Yevamot 3 and many others) as to whether it is two times or three. And in the Halacha there are cases that rule in two and some that rule in three (see the divisions there in the Gemara itself).
Incidentally, in this I explained that all the questions of the latter on various cases of the assumption of three times (as in the Taharat 67) whether it is a sign or a reason, and how a sign is compared to a reason (as in the Maharam of Rothenburg and the R.P. regarding the saying "and rain and dew"), are fundamentally wrong. Sometimes it is a sign and sometimes a reason, and yet one can compare them. The comparison is not because of probability (since probability in any context is different, both from sign to sign and from reason to reason), but because the question is where the halakha draws the formal line. And if it is decided that it passes after a sign, then it is done both in situations where it is a sign and in situations where it is a reason. And from now on, all the recent arguments on this matter have fallen into the abyss, and so on.

And another comment on the rashness you noted. This is just a mistake. Let's say that the line is passed after a sign as you suggested. Now you see a bull that has gored twice. You wouldn't say that it tripped. Isn't this rashness? You have two cases against you, and you still insist? Any decision made in such a situation can be considered rash, whether you pass the line after a sign or after a reason.

If I understood correctly - there is no connection between halakha and matters of the Alma. And regarding the combination of the phenomena that distinguish Am”i, ask things of the Alma, there is a preference for a comprehensive reason of three or two, depending on the case, than to separate. But this is not necessary, it is not factual.
Is the conclusion that there is a reason for Am”i's uniqueness in light of the many special phenomena - is this not too fatal a conclusion in the face of the understanding that it is not factual?

Why is there no connection? There is and there is.
I couldn't even connect two words to the rest of the message.

Combining the special claims of the author creates a solid claim, and it makes more sense to make this claim than to separate the claims - according to the principle of Occam's razor. And despite the combination, it is still not certain, but more logical.
Is it right to base a belief (a significant decision) on common sense, when it is not necessarily true? After all, there is still a chance that everything is coincidental?

Nothing in the world is certain. The fact that an airplane works is based on scientific generalizations, and yet we get on airplanes. And so it is with cars and elevators and medicines and other vegetables.
As humans, we have no escape from uncertainty in everything we think about. Anyone who seeks certainty will not be able to accept any claim. The question of what level of solidity is required is a question that has no clear answer and everyone will give an account for themselves.