Back propagation and Structure of a Neural Network in scikit-neuralnetwork
1) 
From what I understand, scikit-neuralnetwork tries to automatically determine the correct input and output sizes by the X and y data you give it when  calling nn.fit. Therefore structure should be:


Input layer with shape determined by X_train 
Dense layer with 100 units and maxout activation with 2 linear pieces
Softmax classification layer with as many units as needed for y_train 


Seems to use input shape from data here:
https://github.com/aigamedev/scikit-neuralnetwork/blob/b7fd0c089bd7c721c4d9cf9ca71eed74c6bafc5e/sknn/backend/lasagne/mlp.py#L183

And output shape from data here:
https://github.com/aigamedev/scikit-neuralnetwork/blob/b7fd0c089bd7c721c4d9cf9ca71eed74c6bafc5e/sknn/mlp.py#L62

However, note that maxout seems no longer supported: https://github.com/aigamedev/scikit-neuralnetwork/issues/142

2) Yes it uses backpropagation by calling appropriate lasagne/theano functions to create/compile the backpropagation training function:
https://github.com/aigamedev/scikit-neuralnetwork/blob/b7fd0c089bd7c721c4d9cf9ca71eed74c6bafc5e/sknn/backend/lasagne/mlp.py#L50-L103

(Actual training seems to happen here: https://github.com/aigamedev/scikit-neuralnetwork/blob/b7fd0c089bd7c721c4d9cf9ca71eed74c6bafc5e/sknn/backend/lasagne/mlp.py#L316-L335)