לזכות ידי"נ הרב אליעזר זאב בן דבורה וכל ב"ב!!
The gemara [Succah 9] derives from the passuk חג הסוכות תעשה לך שבעת ימים that just as שם שמים is חל on the korban chagiga ["חג"] so it is חל on the succah.
The Rambam learns that this applies to the walls as well as the schach [the Rosh argues and says that it doesn't apply to the דפנות].
A number of questions:
1] The עיקר חפצא of the succah is the schach as evidenced by the fact that the gemara [11b] derives from the passuk חג הסוכות that the schach must be from פסולת גורן ויקב which are גידולו מן הארץ and not מקבל טומאה. So if the succah is defined by the schach then why is there an איסור הנאה on the דפנות?
2] Rav Chaim explains the Rambam as follows: When we talk about the עיקר חפצא of the succah then it only relates to the schach. But when we talk about חלות שם שמים that applies to the walls as well. With regard to שם שמים the determining factor is the KIYUM MITZVA of succah. Of course, to fulfill the mitzva one needs walls and thus שם שמים us חל. What is the logic behind this distinction?
3] According to R' Chaim, the FLOOR of the succah should also be forbidden as the floor is also part of the mitzva as we see later [31a] that if land could be stolen then stolen succah property would be considered a סוכה גזולה. We also see this later [10a] when the gemara insists that the floor of the succah be sturdy enough to hold pillows and sheets because otherwise it is not a succah. But the floor is NOT forbidden?
4] Rashi says [37b] that one may not smell the hadas because we learn that just as succah is אסור בהנאה so is the hadas. But this logic has a flaw! A Succah is more חמור because it is אסור for 7 days unlike a hadas which is only אסור for the first day [מן התורה we only take arba minnim one day].