2941 - The year The Hobbit takes place, marked by Bilbo obtaining the One Ring. The Hobbit ends the same year, I won't spoil anything.
2989 - Moria is recolonized
2994 - Moria is destroyed
3001 - The events of The Lord of The Rings begins with Bilbo giving Frodo the One Ring.
The dwarves "won" the battle at Morias East gate when they "killed" Azog. They just didn't have the numbers to take Moria back. The company of dwarves you see in the movie are not the last remaining dwarves, but rather the ones who take on the quest led by Thorin. The remaining dwarves live in Rhovanion.