What is the ruling on using public services such as transportation and laundromats and evading taxes in a European country that does not recognize Islam, and what is incumbent upon a Muslim in this situation?

A Muslim must be a good role model in adhering to laws that do not contradict their religion, and avoid stratagems that lead to taking what is not rightfully theirs or encroaching upon public or private property. As for taxes, please refer to Fatwa no. 43773.