Properly using activation functions of neural network
How is data predicted from activation functions? (considering that it returns constants on weighted input sum). 


You should consider the fact that the label of your input data is going to be predicted by the network. Moreover, the outputs of the network usually represent the probability of belonging to each class. The label is not predicted by the activation function, it is predicted by the network. Take a network as a mapper which can map the inputs to outputs. The activations are used to add non-linearity in order to approximate complicated non-linear mappings.


  What's the point of multiple hidden layers?


As you can read here, the purpose of adding those is that you can learn different complicated regions. Another interpretation can be this that by adding more layers you can learn more complicated mappings which have non-linear behaviour.

About the global minimum, because you can not see the cost function which is the error based on the weights, due to the fact that it is not possible to visualise it because it has so many dimensions, you should use gradient-descent based algorithms.