The Feast of Tabernacles (or Sukkot or Festival of Booths) as celebrated during the late Second Temple era included elements which were not prescribed in Scripture, and some of which ended with the destruction of the Temple.
The debate between Jesus and the Pharisees about plucking and eating corn did not concern labour on the Sabbath but concerned eating food which was allowed only to priests.
Paul mentions the living sacrifices without explanation, as if the readers would be familiar with the concept. Similar early rabbinic vocabulary suggests that Paul is referring to sacrifices which were given to the Temple but which were inappropriate for offering, because they were female instead of male or for other technical reasons. They could not be un-offered so, although they were sacrifices, they were kept alive as temple property till they became blemished, and any profit from them was for the Lord.