The tefillot of Rosh Hashana- do we add for Rosh chodesh? What about when Rosh Hashana falls on Shabbat? Is there Hallel or mention of joy? Do we make a shehecheyanu?

The nature of Rosh Hashana as a 2 day holiday that is really one long 48-hour period of holiday, applications to the laws of mourning and contrast to yomtov sheini of other holidays

When Shabbat and Yom Tov fall consecutively, application to eruv, laws of Yom Tov, the concept of hachana as a prohibition and as a requirement for preparing before Shabbat and Yom Tov

The principle of breira, its application to choosing which eruv is effective after the fact and questions about the use of parchment set aside for a sefer Torah to be used for non-holy purposes

The parameters and explanation behind the principle of techum Shabbat - is it Rabbinic or Biblical?

When the eruv food is destroyed or lost but it is unclear whether it was destroyed before or after Shabbat began, application to a doubt in the laws of beracha acharona

The effectiveness of an eiruv inside of a house that is locked and nobody has a key- may one break the lock to get in? Can one ask a gentile to do so?

Are tree branches considered to be private or public domain? The prohibition of "moshit"- passing between 2 people and the prohibition of the Levites to see the holy vessels of the mishkan

The concept and parameters of allowing one to violate a minor sin in order to prevent someone from violating a major sin, application to cheyt ha'eygel

The principle of mitzvot lav lehanot nitnu- does this apply only Torah mitzvot or even Rabbinic mitzvot? What is the nature of the mitzvah to comfort mourners and to bring joy to a chattan and kallah?