Early Customs of the Mourners' Kaddish from The Shulhan Arukh-16th Century

(4) Rabbi Yosef Karo, Tzefat, Israel, the Sephardic Rabbi:

Nowadays it is customary that after the closing of the grave with earth has been completed, they [the mourners] remove [their] shoes and sandals, and keep away a short [distance] from the burial grounds and [then] say Kaddish, after which they detach earth [out of the ground] and cast it behind their back and wash their hands with water.

Gloss by Rabbi Moshe Isserles (The Rema), Poland, The Ashkenazic Rabbi:

Some say that [after burial] they sit down seven times because the [evil] spirits follow him, the corpse and so long as they sit down, they, the evil spirits flee from him. And in these countries the custom prevails to sit down only three times after they have washed their hands, and each time [they sit down] they say, 'And let the graciousness of the Lord our God be upon us etc., Ps. XC, 17. 'O thou that dwellest in the covert of the most High etc.

When the corpse is buried on a Festival, one may say thus three times as on a weekday. Likewise, if one was buried close to [the advent of] the Sabbath, this is done [even] on the Sabbath. It is the adopted practice to be particular with one lest he enter another house before he washes [his hands].

One should not take the burial implements, e.g., the spade or shovel directly from another person’s hands. The same applies to the vessel of water used for washing one’s hands.

Those who did not visit the burial grounds for thirty days, say, ‘Blessed be the Lord … who formed you in judgment.’ Siddur. and sits down three times, and the custom of our ancestors is [considered binding] law.

In the Midrashim it is found that one should recite Kaddish. Therefore, it is the adopted practice to recite the last Kaddish [concluding the services for twelve months for a father and mother. Likewise, is it common usage [for a mourner] to recite the Haftarah in the Prophets and to lead the services at the evening prayers at the conclusion of the Sabbath, which is the time when the souls [of the departed] return to Gehenna; and when the [mourning] son leads the Services and sanctifies [the name of God] in public, he [thereby] redeems his father and mother from Gehenna. It is the adopted usage to recite Kaddish for one's mother although the father is still living [and the latter] has no right to prevent his son from reciting Kaddish for his mother.

It is a religious duty to fast on the day that one's father and mother died.

[In the case of] three brothers and a stranger, one who is not their brother although he is a resident in the community, [with respect to the rules of precedence concerning the recital of Kaddish, — the law is that] the three brothers get [priority to recite] three Kaddishim, and the other, the stranger. gets [priority to recite] one Kaddish.

It is customary that when the day on which one's father or mother died, arrives, one always recites the mourner's Kaddish for them. One who knows how to lead the entire Service should do so. However, if there are other mourners [present], it is customary that within the seven days of their mourning [period], they take precedence and he, the one observing the Yahrzeit, has no [priority] rights [regarding] the Kaddish at all; if within [their] thirty [days of mourning], he has [priority rights to recite] one Kaddish. [If] after [their] thirty [days of mourning], — all the Kaddishim of that day belong to him...

...However, during the weekdays, whoever knows how to lead the Services, should do so, and [this] is [even] more efficacious than [reciting] the mourner's Kaddish, which was instituted [originally] only for minors.

And one who knows not how to lead the entire Service, should lead the Service [at least] from [the section beginning with] 'For the chief musician etc., 'And a redeemer shall come to Zion etc.'ובא לציון.

It is the adopted custom to recite Kaddish and lead the Services only for eleven months so that [children] should not consider their father and mother wicked, for the judgment of a wicked person [in Gehenna lasts] twelve months.

If there were mourners present here, i.e., at the Synagogue services, and later other mourners came, the latter have [priority with respect to] the Kaddish and [leading] the Services throughout the thirty days [of their mourning] from the day of burial, even if [the latter] did not hear [the death report until later].

Some say that [in the case of] an apostate Jew who was murdered by heathens, [the law is that] his children recite Kaddish for him.(Having been murdered his sins are forgiven - Siftei Kohen, a commentary on the Shulhan Arukh).