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Q1: it all depends on your application and the amount of training data you have. The advantage of a haar wavelet classifier is that you can easily manipulate parameters throughout the complete process, whereas neural networks are trained and noone has a real idea of how the internal structure looks like. This is one of the main reason why the interest in neural networks has been less in the last couple of years.

Q2: the feature vector is basically the properties from the image you want to use for classification by the neural network. These can be calculated using different techniques which are focussed in the machine learning and the features2D module of the openCV library. You should have a look at the tutorials to see how they actually work.

Q3: this is basically providing a matrix of data to the multiple layer perceptron by using the rows as data vectors and the columns as elements of different images.

However, looking at your questions, I suggest you first go find yourself some documentation on the basic concepts of multilayer perceptrons and how they work, because the questions just illustrate that you have no idea on how it actually works.