Is the shaking of Daled Minim in Jerusalem during exile a Biblical or Rabbinical obligation throughout all seven days?
Some Poskim rule that according to some Rishonim the shaking of Daled Minim in the old city of Jerusalem is a Biblical obligation for all seven days of the festival. Due to this he concludes that one who shakes in the old city of Jerusalem should have intent to fulfill a command which is questionable whether it is Biblical or Rabbinical. Likewise one should be particular to comply to all restrictions that apply to the Daled Minim on the first day of Sukkos when the shaking is Biblical. Hence one is to use a set of Daled Minim that he owns or receive it as a “Matana Al Menas Lehachzir”. Likewise the Daled Minim are to fulfill the validation criteria required for the first day, such as Chasar and the like.
Other Poskim argue that there is no difference between the old city of Jerusalem and other areas.
Must one shake his own personal set of Daled Minim if he is shaking in the old city of Jerusalem?
According to some Poskim one is to use Daled Minim that he owns, or received as a “Matana Al Menas Lehachzir”, throughout all seven days of Sukkos when shaking in the old city.
Must the Daled Minim be Biblically valid for all seven days of Sukkos in the old city of Jerusalem?
According to some Poskim this is required, as explained above.
 Bikureiy Yaakov 658/1 and so agrees Rav Perlo on Taryag Mitzvos; See Piskeiy Teshuvos 658 footnote 2 and 3
 Rambam in Pirush Hamishnayos
 One cannot have intent to fulfill a Biblical command as according to some Rishonim it is Rabbinical even in Jerusalem and hence one would transgress Baal Tosif if he had this intent. One also cannot intend that it is Rabbinical as then he will not fulfill the command according to the Rambam and will transgress Baal Tigara. Hence one should have the doubt in mind. [ibid]
 Tzitz Hakodesh1/47; Kapei Ahron 1/11