Sukkah, K'vi'at S'udah, Pat Habbo b'Kisnin

These 3 related dinim I find puzzling

1. The Mishnah Brurah* says EG that a kiddush in a sukkah using Pat Habbo b'Kisnin [PHBK] can be enough of a k'viut to trigger a "Leisheiv". But apparently this same k'viut on Pat Habbo b'Kisnin fails to trigger Hammotzi and Benching? Why not?

* SA O"ch 639:2 "im kovei'a alav ..."
MB 16 - b'sheim Maamar Mordechai
Beiur Halacha - D"H "Im Kovei'a Alav"

2. The first point above begs the question in general about kiddush bimkom s'udah with a Pat Habbo b'Kisnin; namely why doesn't every kiddush bimkom s'udah trigger a k'viut on eating PHBK, which should in turn require Hamotzi etc.

3. The Major Poskim talk about the case of washing and hamotzi in one place and finishing one's s'udah in another. Yet - Except for a brief blurb in Kitzur SA** - I find little or nothing of the common case when it rains in the middle of a Sukkah meal. Or conversely when it STOPS raining and one moves back to the Sukkah. One would think that this case being common enough would be outlined specifically in the SA, MB etc.

**See EG
SA O"Ch 178 dealing with changes in location. I do not recall seeing any mention the case of Sukkah to House or Vice Versa.

But also see Kitzur SA 135:3 who does address the case of going from the Sukkah to the house re: the first night when it's raining.

Shalom,
RRW