The order of building-Setting up the walls before the Sechach?
One is not to place the Sechach over the [frame of the] Sukkah prior to building the [Halachically valid] walls.
Bedieved, if first placed the Sechach: If one transgressed and first placed the Sechach over the frame and only then built the walls, some Poskim rule the Sukkah is valid. Other Poskim however rule the Sukkah is invalid. [Practically, we rule that the Sukkah is invalid, and one is hence to undo the Sechach and replace it. It suffices to simply lift up the entire Sechach one Tefach and then replace it.]
Building a rim around the frame and then putting up the Sechach: If, however, one first built a rim of the width of one Tefach [8 cm.] around the [entire] top area of the frame, and rests the Sechach on top of it, then it is permitted to place the Sechach over the frame prior to completing the rest of the walls. [Thus, if one is using wooden boards of one Tefach width to create the top frame of the Sukkah [see picture below], then one may rest the Sechach on top of those frames, and then build the rest of the walls.]
One must build the Halachcilly valid walls of the Sukkah prior to placing the Sechach. If one did not do so, he must undo the Sechach and replace it after the walls are built. If one builds a Tefach width rim around the top of the frame then one may place the Sechach over it prior to erecting the remaining walls.
If after building the Sukkah in its proper order, the walls blew off, must one remove the Sechach prior to replacing the walls?
In a case that the Sukkah was erected in the correct order [first walls and then Sechach] then it is not necessary to remove the Sechach prior to fixing the walls, if the walls fell over. However, some Poskim rule that if this occurred before Sukkas one is required to replace the Sechach.
May one use as one of the three Halachically required walls a sliding or removable door?
Using a door that will be opened and closed as one of the three Halachically required walls enters into the above question of causing the Sechach to hover over the Sukkah at a time that the Sukkah is invalid due to the opened door. Practically, as stated above, if at the initial time that the Sukkah was erected, the walls were valid, and the doors were closed, then it is permitted later on to open and close this door, even though it nullifies the Sukkah at the time of its opening. However, according to the stringent approach brought in the previous Q&A, one is to avoid opening the door before the start of Sukkos, and if one does so, is to replace the Sechach. One must note that on Shabbos and Yom Tov it would remain forbidden to open and close this door, being it invalidated, and then validates the Sukkah when opened and then closed.
 Rama 635/1; Hagahos Maimanis Sukkah 5
 The reason: As the Torah requires the Sechach to be placed in a method that deems it valid at the very onset if its construction, however, to place it in an invalid method, and then do an action to make it valid, is invalid due to Taashe Velo Min Hasuiy. Thus, we find, it is forbidden to place Sechahc that is still attached to a tree onto the Sukkah, and then cut the Sechach, being that at the time of its placing, the Sechach was invalid due to its attachment. The same applies even more so here, that since a Sukkah without walls is not considered an Ohel at all, therefore the Sechach is likewise not deemed as valid Sechach. Placing the walls afterwards and turning it into Sechach violates the rule of Taaseh Velo Min Hasuy, and the Sukkah is thus invalid. [Taz 635:4; Levush 635; M”B 635:9; Kaf Hachaim 635:17; See Admur 626:16]
 Bach 635, brought in M”A 635:4; Shiyurei Kneses Hagedola 635; Birkeiy Yosef 635:2 that so is implied from omission of Beis Yosef; Shaareiy Teshuvah 635:3; Beis Hashoeiva 635:11; brought in Shaar Hatziyon 635:12
 The reason: There is a proof from Rashi that such a Sukkah is valid. [Bach ibid, negated in Taz ibid] Likewise, we do not find such a ruling mentioned in any Posek other than the Hagahos Maimanis who records this ruling.
 Levush 626:1, brought in M”A 635:4; Taz 635:4; Eliya Raba 635:4 and that so is found in Sefer Amrakel; Yad Ahron; Bigdei Yesha 635; Beir Heiytiv 635:3; M”B 635:10; Ben Ish Chaiy Haazinu 2; Rav Poalim 1/34
 So rule majority of Poskim and is the seeming conclusion of the M”B and Kaf Hachaim ibid
 See Admur 631:12; 636:3; M”A 636/3; M”B 636/8; based on Michaber 631/9
 Rama ibid; Taz 635:5; M”B 635/11
 Shiureiy Torah p. 249
Other opinions: Some Poskim rule a Tefach is 10 centimeters. [Chazon Ish]
 Taz 635:5
 See Taz ibid that this means that the Sechach contains a one Tefach width of a rim under it.
 The reason: This is similar to the case of “Choteit Begadish” [Rama ibid], in which case we permit one to complete the walls of the Gadish [stalks] if it was put up for the sake of a Sukkah. [See Michaber 635:1; Mishneh Sukkah 1:8] The reason this is permitted is because one is simply adding on to an already existing Ohel. [Taz ibid] As whatever contains one Tefach is considered a valid Mechitza for an Ohel, and this then gives the Sechach that is placed on it the Halachic status of Sechach. [Levushei Serud on Taz ibid]
 Piskeiy Teshuvos 635/2
 Kaf Hachaim 635/18; Pekudas Elezer 630; Mikraeiy Kodesh Sukkos 1:11; Shevet Halwevi 7:56 and 8:146; Shraga Hameir 7:137; See Admur 626:19]
The reason: As the Sukkah was originally made in a Kosher way. [Kaf Hachaim ibid; See Admur ibid]
 Rav Poalim 1:34; 3:40
 Mikraeiy Kodesh Sukkos 1:11; Shevet Halwevi 7:56 and 8:146; Shraga Hameir 7:137; Piskeiy Teshuvos 635:2
 Mikraeiy Kodesh 635:2; SSH”K 24 footnote 115; Orchos Rabbeinu 2 p. 219; Piskeiy Teshuvos 630:3