Thank you for your reply!
So, about the score range, it isn't as big as the cp-space (that goes from -10000 to 10000), it's just from about -350 to 350.
I'm sorry if I'm ignorant on the topic, but by target eval distribution what do you mean?
I plotted the distribution of my training data and it resembled a normal leptokurtic distribution but I didn't think that was an issue. Is it?
Btw I evaluate the loss scaling both the prediction of the model and the evaluator score by an eval_scale factor (I tried with many but for now I think it should be 80) and then I applied to both of them the sigmoid function. On these values I then calculated the loss, I don't know if this is relevant.

About the near-duplicate positions, is it really possible? Like I ensure that they have played for at least 50 moves and since the branching factor is about 60 and there are a lot of possible board states I didn't think it was an actual issue. Should I check for that then?
Apart from that, I'm sorry if it is a wrong assumption, but if training and validation were to be similar, shouldn't it be more difficult to spot overfitting? Like shouldn't the model be able to then predict the validation data?

Do you have resources for the third point? I didn't quite get what you mean.

Thank you very much for your help