is a 4 output regression equivalent to 4 single output regression superposition?
"My question is : can I consider that all of my outputs are unlinked"


No, in general you can't, unless you have prior knowledge indicating so. There is a high chance that your outputs are correlated. To explore linear correlations, perform a correlation analysis (calculate correlation matrix). To investigate nonlinear relations, calculate the distance correlation.


  and if yes, is it true to imagine that I can perform 4 regressions in
  parallel (one for each output) to make an equivalent 4 ouput model ?


If your analysis proves that there is low correlation between the outputs, only then you can implement 4 independent regression models in parallel with meaningful results.

My suggestion would be to implement a MIMO machine learning model (multiple inputs / multiple outputs), such as a multivariate Recurrent Neural Network.

Hope it helps :)