Motzei Yom Kippur

Questions on Motzei Yom Kippur:

1. Why do people wish each other Gut Yom Tuv or a gut kvitel or Piska Tova?
2. Why do people straight away do Kiddush Levana while still fasting when after Tisha BeAv you must wait until after eating? How can you say it without proper shoes on?
3. Usually after a fast one must not eat a meaty meal. However, on Motzei Yom Kippur people are meant to have a meaty meal?
4. People start on Motzei Yom Kippur building their Sukka. Why the rush when then still have five days until Sukkos?
5. The Kohen Godol would make a special feast for his friends on Motzei Yom Kippur. Why?

Ideas for answers on Motzei Yom Kippur:

1. The greeting of Gut Yom Tuv is because of the special time of Motzei Yom Kippur. Tosfas Yuma 87b brings that a Bas Koil goes out urging people to join in a festive meal. The meal following the fast takes on the status of a semi-Yom Tuv. The Rosh (on Brochos 26a) brings that there is a mitzvah to prepare a seuda on Motzei Yom Kippur since it is like a Yom Tuv. This is based on a Midrash that says that a Bas Kol goes out saying: Go out and eat with happiness your bread (Koheles, 9:7). This shows that this time is a time of rejoicing. With regards as to why people greet with a gut kvitel or Piska Tova this is in reference to the last stage of din that comes after the judgement of Yom Kippur. The time of Hoshana Rabba is when the messengers are sent out to carry out the final decrees.
2. The idea of not saying Kiddush Levana when fasting is that it should be said in a happy state. After Tisha BeAv we are in a sad state and therefore we must eat and change into shoes before reciting it. However, the fast of Yom Kippur is not one because of sadness but is rather to elevate us spiritually. Therefore this state is one of happiness and therefore on Motzei Yom Kippur we can straight away recite Kiddush Levana despite being in a state of fasting and not having proper shoes on.
3. The idea again is that after a fast the mood continues being sad and therefore a meat meal that is associated with happiness should not be eaten. However, since we explained that the fast of Yom Kippur is not out of sadness and on the contrary is one of happiness therefore this is reflected how on Motzei Yom Kippur a meaty happy meal can be had.
4. This is to show how we are changed people over Yom Kippur. We want to show how we now desire to do what Hashem wants that is seen in the mitzvos. Even though we have five days until Sukkos, the making of the sukka right away shows how we are eager to do the mitzvos and please Hashem.
5. The Kohen Godol was faced with death when he entered the Kodesh Hakodoshim on Yom Kippur. His surviving this shows that he must be worthy and on a spiritual level and therefore is a cause for celebration. Perhaps this is similar to someone who is faced with death and is saved makes a celebration to remember this miracle.