The ReLu is a non-linear activation function. Check out this question for the intuition behind using ReLu's (also check out the comments). There is a very simple reason of why we do not use a linear activation function.
Say you have a feature vector $x_0$ and weight vector $W_1$. Passing through a layer in a Neural Net will give the output as
$W_1^T * x_0 = x_1$
(dot product of weights and input vector). Now passing the output through next layer will give you
$W_2^T * x_1 = x_2$
So expanding this we get
$x_2 = W_2^T * W_1^T * x_0 = W_2^T * W_1^T * x_0 = W_{compact}^T * x_0$
Thus as you can see there is a linear relationship between input and output, and the function we want to model is generally non-linear, and so we cannot model it.
You can check out my answer here on non-linear activation.
Parametric ReLu has few advantages over normal ReLu. Here is a great answer by @NeilSlater on the same. It is basically trying to tell us that if we use ReLu's we will end up with a lot of redundant or dead nodes in a Neural Net (those which have a negative output) which do not contribute to the result, and thus do not have a derivative. Thus to approximate a function we will require a larger NN, whereas parametric ReLu's absolve us of this problem,(thus a comparatively smaller NN) as negative output nodes do not die.
NOTE: alpha = 1
will be a special case of parametric ReLu. There must be a balance between the amount of liveliness you want in the negative region vs the linearity of the activation function.