a) Combining quarks into hadrons in different ways leads to different properties of the resulting bound state. The mass is an obvious example. Unfortunately, while rather easily accessible experimentally, it is hard to predict the mass of bound states with high precision in QCD (the theory describing the strong force). Others properties can be more powerful here. For example the intrinsic angular momentum (spin) and the parity of the bound state. The decay product trajectories from particles with different spin/parity will show different angular distributions. By measuring these distributions one can rule out certain combinations.
b) In general what would be required is someone working out in more detail how these predicted particles would interact with known particles, in this case charm and strange quarks. I just read through the article you linked to. According to the article, all predicted particles are gauge bosons, i.e. they introduce new interactions. The number in the name Y(4140) refers to the mass measured in MeV. A gauge boson with such a low mass coupling to quarks would have been noticed already. Furthermore, the reported observation does not hint anything exotic. Just something that is perfectly allowed in the Standard Model, although not fully understood in its dynamics yet. So I'm afraid, no, this is not a candidate for your favourite model.