If you had guests for Yom Tov, they cannot take food from you out of your techum unless they owned the food before Yom Tov.

You can only feed animals that come to live in the city, animals that live outside are considered muktza and cannot be fed.

Rosh Hashana 1:1

The first day of the month of Nissan was used to count the years of rule for a king, to know how long the king has been king. This was used for dating contracts as they would say they happened in such and such year of this king.

The month of Nissan starts the year in reference to counting Yomim Tovim. This means the prohibition of not bringing karbanos late, is three Yomim Tovim starting from Nissan.

The first day of the month of Elul starts the year for maaser of animals. All animals born before are considered one group and if you have 10 you give one as a korban. R’ Elazar and R’ Shimon say for this the new year is the first of Tishrei.

The first day of the month of Tishrei starts the year for counting when the shmitta and yovel [ the 50^th jubilee year] year starts. The year for orlah [the first three years of a tree when the fruit are forbidden to be eaten] starts also from the first day of the month of Tishrei. For the law relating to Tithes which cannot be given from one years produce on the next, the year starts from the first day of Tishrei.

The first day of the month of Shevat starts the year for the trees in reference to counting the years of netai ravai, which is the 4^th year when the fruit starts having laws like maaser sheni. This is according to Bais Shammai but Bais Hillel says it is the 15^th day of Shevat.