The law if Non-Kosher Sechach [Tree or ledge] is hovering over ones Sukkah:
A. The shade must come as a result of Kosher Sechach:
Just like by the clouds of glory it was the actual clouds which gave us shade from the sun, similarly a Sukkah is only valid when the Kosher Sechach gives the shade.
Remove all interferences between sky and Sechach: [For this reason one is to verify and remove any interference that rest between the Sechach and the sky, such as a tree which hovers over the Sukkah.]
B. The law if non-Kosher Sechach hovers over the Sukkah, such as a tree hovering over a Sukkah:
First Opinion: If an item which is not Kosher for Sechach hovers over the Sukkah, then if there is so much non-Kosher Sechach which hovers to the point that if all the Kosher Sechach directly under the hovering non-kosher Sechach were to be removed then the Sukkah would not contain more shade then sunlight, then it is invalid. Thus we view all the Kosher Sechach under the non-kosher Sechach as non-existent.
However if there would still remain a majority of shade over sunlight in the Sukkah even if we were to remove all the kosher Sechach directly under the non-Kosher Sechach then the Sukkah is still valid, as it nevertheless contains the necessary amount of shade. [See Q&A 1]
Other Opinions: However there are opinions which say that we do not view the kosher Sechach directly under the non-kosher Sechach as non-existent, and rather the Sukkah remains Kosher, even if there is so much non-Kosher Sechach which hovers over the Sukkah that it alone can give majority shade, as long as the Kosher Sechach alone is also capable of producing majority shade in the Sukkah. However if the Kosher Sechach alone cannot give majority shade and it only does so together with the non-Kosher Sechach then it is invalid. [See Q&A 2]
The Final Ruling: The main Halachic opinion is like the former. Nevertheless by a time of need, such as there is no other Sukkah available, and it is not possible to remove the hovering non-Kosher Sechach, then one may rely on this latter opinion in order so one not nullify himself from fulfilling the Mitzvah of Sukkah. [See Q&A 3]
The hovered area is considered to not be covered by any Sechach, and if due to this the Sukkah would have more sunlight then shade, then the Sukkah is invalid. Although in a case of need, it is better to eat in such a Sukkah rather than nullify the Mitzvah.
Must one initially build the Sukkah completely under the sky, not having any non-kosher Sechach hovering over it, even if it is not enough to invalidate it?
Some Poskim rule that one is to initially build the entire Sukkah under the sky and not have non-Kosher parts hover over it, even if it will not invalidate it.
Does Non-Kosher Sechach, such as a hovering tree, which is over 20 Amos high, invalidate the Sukkah if the above conditions are not met?
If a tree or wall is standing next to ones Sukkah and gives it shade to the point that even if the Sechach were to be gone there would still be shade in the Sukkah, is the Sukkah valid?
Yes. So long as the Sechach is directly under the skies, it is valid, irrelevant to whether or not there are other reasons that there would anyways be shade.
If a tree near the Sukkah blows with the wind which causes it to hover over the Sukkah, does it invalidate the Sechach under it?
If a hot air balloon or plain, or helicopter hovers over one’s Sukkah, does it invalidate the Sechach under it?
Yes, according to those Poskim that invalidate the Kosher Sechach even if the hovering is 20 above. However according to those Poskim which are lenient, as explained above, then in this case as well it would be permitted.
If laundry lines or electric wires hover over ones Sukkah, do they invalidate the Sechach?
If the individual lines/wires are not within three Tefachim [24 cm] of each other, then they do not invalidate the Sechach.
If they are within 3 Tefach of each other then: Some Poskim rule that one is to suspect for the Bach which holds Levud Lehachmir and thus the Sukkah is considered to be under a non-kosher roofing for the entire circumference of the hovering lines. [See footnote for opinion of Admur] Others however limit this stringency of the Bach to a case when all the hovering items if were to be placed adjacent to each other they would take up 4 tefach [32 cm], which is not the case by lines, and thus in the above scenario it would be permitted according to all.
If there is laundry over the lines: This does not invalidate the Sukkah so long as the laundry is hanging down vertically, as opposed to spread horizontally over the lines. When hanging vertically it is allowed even if the clothing blow with wind and thus at times spread horizontally over the Sukkah. If however the cloths were spread horizontally or due to wind got stuck on another line and are now spread vertically, then that area invalidates the Sechach under it.
If there is snow over ones Sechach, does it invalidate the Sechach under it?
Some Poskim rule that it is a kosher roofing and thus the Sukkah remains valid. Others rule that the Sechach under it is invalidated [and thus if due to this there is not more shade over sunlight within the Sukkah, then the entire Sukkah is invalid]. The Chabad custom follows this stringent opinion even on Shemini Atzeres. One is to thus remove the snow before eating in the Sukkah. On Shabbos one would hint to a gentile to do so for him.
 Piskeiy Teshuvos 626/1
 Kaf Hachaim 626/6
 Beis Meir
 Magen Avraham 628/2
 Biur Halacha 626 “Tachas Hailan”
 Daas Torah, brought in Piskeiy Teshuvos 626/2
 The reason: As since the tree is moving with wind it is not defined as a tenting [of which must be permanent], and only a hovering which is defined as a tenting can invalidate the Sechach.
 Daas Torah brought in Piskeiy Teshuvos 626/2
 Now, although it moves and is not a set hovering, nevertheless since its movement is due to man and not wind, it retains a tent status.
 Piskeiy Teshuvos 626/8
 M”B 626/17
 Tzaruch Iyun regarding if Admur would rule Levud Lehachmir in this case. On the one hand he makes no mention of such a concept anywhere in the Halachas discussing making a Sukkah under a tree or under non-kosher house frames. This thus implies that it is a non-suspicion. On the other hand he mentioned regarding the scenario of placing Sechach over the non-kosher frames that it is not a problem of levud even when within 3 tefach of each other being that the sechach is in between them. This implies that when there is no Sechach in between then we do suspect for levud.
 Kinyan Torah, Rav Wozner, Rav SZ”A.
 Minchas Yitzchak 8/9
 Pashut, Rav Wozner
 Piskeiy Teshuvos 626/3
 Beir Heiytiv 626/1; Shaareiy Teshuvah 626; Birkeiy Yosef 626/7
 As snow does not receive impurity and is not attached to the ground.
 Aruch Hashulchan 629/2; Ruling of Admur, brought in Likkutei Dibburim 2/25, regarding the snow storm of 1787 in Liozna that the Chassidim would remove the snow prior to eating
 Ruling of Admur, brought in Likkutei Dibburim 2/25, regarding the snow storm of 1787 in Liozna that the Chassidim would remove the snow prior to eating.
 Likkutei Dibburim 2/25