Difference between Conv and FC layers? What is the difference between conv layers and FC layers?
Why cannot I use conv layers instead of FC layers?
 A: A convolutional layer applies the same (usually small) filter repeatedly at different positions in the layer below it. E.g. if the input layer has dimensions 512 x 512, you could have a conv layer that applies the same 8 x 8 filter (specified by 64 filter coefficients), at each point in (e.g.) a 128 x 128 grid overlaid on the input layer. On the other hand, each node in a fully connected layer would learn 512 x 512 weights, one for each of the nodes in the input layer. 
Conv layers therefore are well suited to detect local features that may appear anywhere in the input (e.g. edges in a visual image). The idea is that you don't have to train every node separately to detect the same feature, but rather you learn one filter that is shared among all the nodes.  
(Note that each conv layer usually learns a set of several filters, each of which gets applied repeatedly across the input. E.g. if the conv layer learns 16 different features, it is said to have a 'depth' of 16.)
FC layers are used to detect specific global configurations of the features detected by the lower layers in the net. They usually sit at the top of the network hierarchy, at a point when the input has been reduced (by the previous, usually convolutional layers) to a compact representation of features. Each node in the FC layer learns its own set of weights on all of the nodes in the layer below it. 
So you can (roughly) think of conv layers as breaking the input (e.g. an image) up into common features, and the FC layers as piecing those features together into e.g. objects that you want the network to recognize.
A: You can use conv layers for instead of FC. However, due to the nature of conv layers where weights are shared, there will be much less parameters. It may cause that your network may not be capable enough to learn the stuff. But it all depends on your network. 
A: Convolutional and fully connected layers are the building blocks of most neural networks. They are the units (layers) that most NNs are constructed from.
Convolutional and fully connected layers are multiplication parameters that connect one layer of neural network to subsequent layers, thereby making each layer’s weights as a linear combination of its previous layer (nonlinear after applying Relu or Tanh). They differ however in the way that they connect two layers of a neural network.
As the name suggests, fully connected layers connect each neuron of the output layer to each and every neuron of the input layer. They can serve in order to express any general pattern in the input layer. This enables fully connected layers best to be capable of recognizing global patterns in a NN layer. Therefore, they are well suited for being applied to wrap up all the patterns recognized with all previous layers (as the final layer of NNs). Also, the size of the layers at the final layers of NN is often relatively small, which means that the high number of parameters within a fully connected layer is less of an issue when it comes to learning. However, the abundance of the number of the weights (that should be learned independently in learning the NN), as well as potential problems such as over-fitting can hinder them from being the ubiquitous solution in NN architectures.
On the other hand, in convolutional connects each neuron of the output layer merely to a handful of the neurons (locally) in the previous layer via a universal “filter” that makes the number of the parameters to be learned really less than a fully-connected layer. Additionally, the uniqueness of the filter applied to the whole neuron layer allows for the convolutional layer to recognize recurrence of the same pattern in different input layers (coincidence of letters in text processing and corners in image recognition). Accordingly, They can more easily be stacked in order to construct deep neural networks with affordable learning processes due to the low number of parameters to learn.
