Commonly you divide the domain up into different accuracy,stability regimes and apply a different approximation within each.
For $|x|<1$ you can use a polynomial approximation, like Chebyshev. For $1<|x|\leq E$, $E$ depending on implementation of the formula, you can use a related formula to the one you described.
For $|x|>E$ you can use $\tanh(x) \...
YOLO architecture uses the softmax activation function determining the classes of objects in bounding boxes in the output layer. But from the code you have shared, sigmoid is used in the last layer for prediction. It seems that you're trying to implement YOLOv3.
Please look at this paper original paper. This will help to give a better understanding.
The activation functions are used in hidden layers and output layer. The output layer will usually have sigmoid or softmax activation while hidden layers usually use ReLU. ReLU is available in Orange at least (there is a dropdown which you can explore but ReLU works best mostly, read this). Also, check this link for looking at neural networks in Orange.
Yes, it is pretty much possible that you can have an in-active neuron in an output layer.
Nodes at the input layer called passive nodes
Nodes at hidden layer called active nodes or unobservable outputs
Nodes at output layer called observable outputs