Learn the Gemara “דף מד. “א”ל אביי (seven lines from the top of the Amud) until אלא אמר רב זביד
The Gemara presents three answers as to why Aravos (Hoshanos) are only taken one day זכר למקדש even though in the Beis Hamikdash aravos were taken all seven days of Sukkos.
Questions:
In the first proposed answer does Rava believe that indeed there is a Mitzvah to take aravos all seven days of Sukkos זכר למקדש?
In the final answer of the Gemara why does the fact that there is no Mitzvah from the Torah to take aravos outside of the Beis Hamikdash affect the decision of instituting a mitzvah of Aravah all seven days זכר למקדש as was done in the Beis Hamikdash?
See ריטב”א “מאי שנא https://www.sefaria.org/Ritva_on_Sukkah.44a.1?lang=bi
Learn רמב״ם הלכות לולב פרק ז הלכה כא-כב and מגיד משנה
https://hebrewbooks.org/pdfpager.aspx?req=14278&st=&pgnum=287
Major Question:
The Rambam seems to offer an entirely new reason than the Gemara as to why mitzvah the of Aravah is only one day זכר למקדש?
Learn ערוך לנר for an explanation for the Rambam
https://hebrewbooks.org/pdfpager.aspx?req=14414&st=&pgnum=171
According to אבא שאול the mitzvah of Aravah in the Beis Hamikdash is learnt from the words ערבי נחל
Learn תוספת דף לד. “ואחת who asks where in the pasuk is it indicated that it’s limited to Beis Hamikdash?
See תוספת ראש
https://hebrewbooks.org/pdfpager.aspx?req=14724&st=&pgnum=60
And ערוך לנר
https://hebrewbooks.org/pdfpager.aspx?req=14414&st=&pgnum=125