I've never seen this yellow star on the training page.

Does it exist? And if so when do we get it?

What about the player's talent. How does that effect the training?
Talent has no direct influence on training as such. It does however limit how high a player can reach in his skills. If a player has talent;
1 then his maximum is 11
2 then his maximum is 12
3 then his maximum is 13
4 then his maximum is 14
5 then his maximum is 15
6 then his maximum is 16
7 then his maximum is 17
8 then his maximum is 18
9 then his maximum is 19
10 then his maximum is 20

The only 3 exceptions to this rule are speed, strength and stamina. Speed and strength are limited by a hidden maximum value (different for each player) that represents the maximum value player can reach even if he trains with weights each and every day. Stamina is not limited at all, and with extensive physical (fitness) training every player can reach 20 in stamina.

Is it possible for a player to go above his maximum?
It is possible, it's just that much harder for the player to achieve that.
If a player is at his maximum then he has 1 in 3 chance to gain a point/level.
If a player is at his maximum + 1 then he has 1 in 5 chance to gain a point/level.
If a player is at his maximum + 2 then he has 1 in 10 chance to gain a point/level.
If a player is at his maximum + 3 then he has 1 in 20 chance to gain a point/level.
It is impossible for a player to go more than 4 above his maximum.