How old should be my bitcoins to send them again without transaction fee?
As the coins "age" they will have a higher priority.

I don't know the algorithm, but believe it is roughly like a day or so and then the age of the coin no longer is a factor.

So if you are seeing minimum fees for coins more than a day after you've received them, it is because of other reasons, such as having outputs at amounts below 0.01 BTC.