On the inputs and outputs of auto-encoder neural network

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I am reading about autoencoder these days. Autoencoders actually reconstruct the original input and also help in dimensionality reduction as below :

At encoder:

X : the input data

c: the resulted code after encoder.

At decoder:

c: The input data

X' : is the output where (X - X') should be almost equals to 0.

My question is about the input X and c. What should it be ? can X be binary data or decimal ? .. the same of C, can it be binary? or it must be decimal.

The other thing, encoder and decoder must be together or we can use them separately? I mean we use the encoder to get the output of encoder c, and then we can modify or change c then we use the decoder, Is that possible? What's the percentage of c compared with X, .. I mean the size of c should be half, quarter the size of X ? or it can be whatever ...

Thank you.

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