Is the Fast of Tevet considered a 24 hour fast, or does it begin in the morning until early evening?
Only Yom Kippur and Tisha b'Av are 25-hour fasts. The others are minor fasts, from dawn (first light, before sunrise) until nightfall (full dark). The minor fasts are:
- Fast of Gedaliah (3 Tishrei)
- 10 Tevet
- Fast of Esther (13 Adar)
- Fast of the Firstborn (for those to whom it applies) (14 Nisan)
- 17 Tamuz
You can read more about these fasts at Judaism 101.