I have 3 graphs of a binary Logistic Regression that I want to understand better what is happening and learn of a strategy to make the model better
Given a confusion matrix:

            predicted
            (+)   (-)
            ---------
       (+) | TP | FN |
actual      ---------
       (-) | FP | TN |
            ---------


we know that:

Precision = TP / (TP + FP)
Recall = TP / (TP + FN)



  As can be seen in the images, as the threshold is increased there's a
  certain point it stops predicting


Thats not true, it stops predicting accurately only one class. What is udnerstandable because you moved threshold to make all your predictions on the other class. 

Dont optimise this yourself, for example random forest will do this for you imiplicitly, (determining cut-off level) or just do hyperparameter optimisation youself.