What is the appropiate position for the 'Acknowledgements' in a paper? Are there policies by (mathematical) journals where to put them?
Furthermore, is it common to make acknowledgements a \paragraph (in Latex), rather than a \subsection or a final \section?
Acknowledgements generally go a separate section after the conclusion. You can see the Elsevier advice on acknowledgements sections here. If you have a specific conference or journal you are submitting to, and want to know what other authors have done, browse some of the previous volumes' papers or proceedings.