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Who says Rebbi said Kiddush?

I read the following statement on the Chabad.org website https://www.chabad.org/calendar/view/day.asp?tdate=12/9/2022

"The Talmud (Ketubot 103a) relates that even after his passing, for a time, Rabbi Judah would still visit his home every Friday evening at dusk. Wearing Shabbat clothes, he would recite the Kiddush, and thereby discharge his family members from their obligation to hear Kiddush."

I saw a similar claim on the Jewish Press https://www.jewishpress.com/judaism/halacha-hashkafa/the-death-of-rebbi/2012/11/02/

"And so we are told that each Friday night when _Boi B’shalom_ was recited, he would return home, sit at the Friday night table and say Kiddush for his family."

I looked up https://mechon-mamre.org/b/l/l3212.htm Ketubot 103a and found

 כל בי שמשי הוה אתי לביתיה ההוא בי שמשא אתאי שבבתא קא קריה אבבא אמרה אמתיה שתיקו דרבי יתיב

and this is the English I https://www.dafyomi.co.il/kesuvos/points/ks-ps-103.htm found:

Every week, when Shabbos entered, Rebbi returned to his house.

Once, a neighbor called on the porch and Rebbi's slave asked her to be quiet, lest she disturb Rebbi.

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On the same dafyomi site, under the https://www.dafyomi.co.il/kesuvos/review/ks-rg-103.htm?q=0 "full review" there is

"Rebbi also commanded his sons to make sure that a lamp would always be lit, the table laid and the bed (or the couch) made at dusk (of Erev Shabbos), because he initially used to arrive at his house then and to recite Kidush on behalf of his household (even though strictly speaking, he was no longer alive)."

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I looked in Rashi and Tos'fot and saw nothing which would add in the whole "say kiddush" part - Rashi explains _bei shamshei_ as the onset of Shabbat but that's it. It just seems to be that he visited his house.

So:
1. From where do we learn that he said kiddush
2. From where do we learn that he said it to "discharge his family members from their obligation to hear Kiddush"
3. How can a dead person (who is not obligated in mitzvot like kiddush) discharge the obligation of others?