Mishnah and Psalms by Graves

Is it permissible to study Mishnah and recite Psalms for the merit of the deceased at their grave, or is it forbidden due to mocking the poor?

Since this is done to honor him, it is permissible to recite Psalms. Even though there are other graves nearby that are not honored in this way, it can be explained that it is pleasing to them, as people come to study Torah at their graves to honor them. Some are particular to say before starting the Psalms that they are for everyone within four cubits.

Regarding Mishnah, Ashkenazim tend to be stricter, while Sephardim are more lenient.

The Talmud, Tractate Berakhot, page 3b: "Rabbi Zerika said in the name of Rabbi Ami, who said in the name of Rabbi Yehoshua ben Levi: one should not speak in front of the dead except for the words of the deceased."

In II Chronicles, chapter 32, verse 33, it is written: "And Hezekiah slept with his fathers, and they buried him in the ascent of the tombs of the sons of David, and they honored him at his death." In Bava Kamma, page 16b, it is said: "And they honored him at his death - this teaches that they established a yeshiva at his grave."

Tosafot writes there: "And not on the grave itself but at a distance of four cubits, so as not to mock the poor."

However, in the Nemukei Yosef, it is brought in the name of the Rama to answer Tosafot's question why it is not considered mocking the poor, and it is written: "Since it is done for his honor, it is permitted."

Thus ruled the Shulchan Aruch, Yoreh De'ah, Siman 344, Se'if 17: "It is permitted to recite verses and give a sermon for the honor of the deceased, within four cubits or at the cemetery." Responsa Radbaz, Part 1, Siman 224: "The words of the deceased are eulogy, justification of judgment, rebuke, and similar matters, all are called words of the deceased and are permitted to be said within four cubits of the deceased. But to answer Amen to Kaddish or to say Barechu and similar matters, which are considered mocking the poor, is forbidden. And it is unnecessary to speak words of Torah, which are considered mocking the poor. And it is not written to permit words of Torah for the honor of the deceased."

Birkei Yosef, Yoreh De'ah, Siman 344, Law 14, writes: "And even today, this is the custom in most Jewish communities - both to give a sermon in front of the deceased and on the grave, and to study on the grave for his rest. I also saw that the great traveler Radbaz wrote in the new responsa, Siman 224: "Regarding one who gives a sermon for the deceased before him, it seems there is no concern of mocking the poor, since it is done for his honor." And he explicitly wrote to permit studying on the grave for his rest, and this is the custom of the Sephardim.