When the Talmud in Yoma discusses whether one may save someone who is possibly a non-Jew and possibly a Jew, is that because if he is a non-Jew then he also behaves in an inhuman way, even though he himself does not know that?

Indeed. That is a Talmudic passage at the beginning of tractate Ketubot, not in Yoma.

“But didn’t we learn: If they found there an abandoned infant, if the majority are Cutheans, he is a Cuthean; if the majority are Israelites, he is an Israelite; if it is half and half, he is an Israelite. And Rav said: They taught this only with regard to keeping him alive, but not with regard to establishing his lineage. And Shmuel said: As for clearing away a heap of rubble for him, when Shmuel’s statement was stated, it was stated on the first clause: if the majority are Cutheans, he is a Cuthean. Shmuel said: But with regard to saving life, it is not so.”
Yoma 84b–85a

Sorry. I remembered only the parallel passage in Ketubot.

Is a Jew who behaves in an inhuman way (like the non-Jews in the time of the Sages) forbidden to be saved on the Sabbath?

The intention is probably extreme inhumanity, like idolatry and other foolishness and rare forms of wickedness.

Apparently, by Meiri’s time this had already largely passed from the world among non-Jews, all the more so among Jews.

There isn’t such wickedness and stupidity nowadays.

The discussion is about the fundamental issue (which has practical relevance to my first question).
P.S. Meiri’s name was Menachem.

With regard to Jews, there is a presumption that one does not behave that way. Jewish law works according to the majority and the reasonable person. But even in Jewish law, if someone is not “one of your people in deed,” there is no obligation to save him.

Another question: it says, “do not stand idly by your neighbor’s blood”; from here it seems that a Jew is called “your neighbor,” and a non-Jew is not. Only a Jew one is obligated to save from death, and not a non-Jew, because he is not “your neighbor.” That would mean that even on a weekday it is forbidden to save a non-Jew from death, according to what I read. What is the explanation for that?

Question 2: It says in Maimonides that if a person’s father dies and he did not keep the commandments, it is forbidden to mourn for him, and one should wear white clothes and rejoice. What is the explanation of this Jewish law? It is far too extreme a law to actually observe.

The explanation is that toward someone who behaves like an animal, there are no obligations. A non-Jew who behaves properly must be saved, and according to Meiri, even on the Sabbath.

As above.

You are looking at it anachronistically. In the past, someone who did not keep the commandments was considered wicked.

Okay, what exactly is meant by animal-like behavior?
So according to what you’re saying, a wicked person in earlier times was identified with animal-like behavior? And therefore one has no obligations toward a wicked father?

Second question:
I saw a quote from Maimonides: heretics and sectarians who deny the Torah—it is a commandment to kill them; if one can, one should kill them by the sword.
If an unbeliever fell into a pit, one does not save him. This also very much requires explanation.

Third question:
When there is litigation in a religious court between two people over ownership of a certain piece of property, and the religious court did not decide to whom the property belongs, do both people have permission to use violence in order to seize the property by force, even if the one who took it is not actually the owner?

It means immoral behavior and sometimes behavior that is actually wild. I have nothing to add.

As above.

That depends on the circumstances. It is a complicated topic, and if it interests you, you should study it in depth. Certainly, in no case is someone who is not the owner of the property permitted to take it.