Confusion regarding the Working mechanism of Activation function
I think following picture by Rubens Zimbres can express how this process will be done except loss function part:



  Is there a binary step function in the output layer which squashes the values of the linear combination of weights and and inputs to 0 or 1?


Answer : Yes if you consider following example shows how Sigmoid squishes values to be between 0 and 1:



  Does classification means always applying a thresholding function on top of a linear or non-linear function which is in the hidden layer?


Answer: It does.


  Say the predicted output value is 0.75 and actual Y is 0. Then, how is 0.75 converted to 1? The loss function would calculate the error as actual - predicted = 0-0.75 = -0.75


Answer: Loss function and calculation of error for classification-based NN is not just by computation of  $Y_Actual - Y_prediction$ 

but It is used normally by combination of Softmax activation function and cross-entropy as follow:


See the whole training process Multinomial Logistic Classification $D(S(wx+b),L)$