Is it permissible for a traveler who is visiting relatives and spending his time playing to shorten and combine prayers, knowing that the visit might only be to see the relatives if playing is not possible?

It is permissible to shorten (qasr) and combine (jam') prayers during travel if the distance is that which allows for qasr, and it is permissible to do so during a temporary stay (less than four days). Committing sins in the place of travel does not prevent one from availing themselves of the dispensations. So, whoever travels a permissible journey and then sins during it, may still avail themselves of the dispensations. However, whoever travels for the purpose of committing a sin may not avail themselves of these dispensations. Al-Buhuti said: "No dispensations are granted for a journey undertaken for the purpose of sin... And one may shorten prayers if they begin a journey, even if they sin during their permissible journey."