1. On the first and the last picture (shot Silvester night, 31XII2008), is Moon coming to the first Phase.
2. In the middle Moon is coming to the first Phase too, but this is next cycle of our natural Satellite.
3. Star? This is probably the "Evening Star", planet Venus (or Venera), in the west elongation to the Earth.
Some things, like the Moon, have similar names in many languages. So tell us the name of the Moon in Your language!
Polish: "Księżyc" (meaning: "Son of Prince, the Sun") <- original as usual ;