Is a neural network (for example a MLPClassifier in Python) able to learn to map a completely (or very) different input feature set to the same output class? Or is it better to work in this case with more than one output class and map these recognized output classes afterwards to the same class manually?
Yes, neural networks excel at finding highly non-linear decision boundaries. For example, take a look at this demo (don't forget to click the play button to make the network learn). Even this very simple network is able to learn that the opposite corners of the input space belong to the same class.