Simple Neural Network -- learning machine learning by brute force [closed]

I am making my first steps in machine learning and today I have taken a code from this blog post, compiled it and ran, here is the repository. I have fed it csv MNIST from here. Seems like it is doing something.

I do not get what is going on here even at 10% level though.

1. Class "NeuralNetwork" has been defined in .hpp as an object with two dependancies but in main.cpp it, for some reason, is ok with taking just a topology vector in.
2. topology vector seems to be valid only if first layer has 2 neurons and last layer - 1. Why?
3. Function "traning" has some print statements. The counter in the loop is constrained by the size of "input_data". This size for some reason 1000. SHouldn't it be 60,000 (MNIST data set size)?

Thanks=)