The Mishnah and Gemarah (Succah 19b) discuss a case of a succah that doesn't have a flat roof:
מתני׳ העושה סוכתו כמין צריף או שסמכה לכותל ר' אליעזר פוסל מפני שאין לה גג וחכמים מכשירין
MISHNA: One who establishes his sukka like a type of circular hut,
with no roof whose walls slope down from the center or who rested the
sukka against the wall, by ...
I am not sure I understood the deepness of the question. But the Rash quotes the Gemara Eruvin 27b in which the exclusion of water and salt for maaser sheni is learned from drashot. One of them is cited by the Rash, Klal Ufrat Uchlal. For maaser sheni the necessary conditions are not only gidule Karka, but Peri Miperi Ugidule Karka or, following another ...
Schach is muktzeh therefore cannot be fixed by a Jew during chag or Shabbat, but can be fixed during hol hamoed.
See for instance this digest of Sukkot laws
If Schach blows out of place on Yom Tov, one may not fix it, since the
Schach is Muktzeh. However, if the Sukkah is no longer Kosher (or its
status is questionable), one should consult with a Rov ...