Those offenses listed on the pink summonses can indeed cause a problem down the road.  Some of them are misdemeanors in New York. As an fyi, in New York records can not be expunged.  Instead they are sealed.  But the records can indeed be seen by certain parties - such as law enforcement - in a background search.  Please go and seek legal counsel.  The charge and disposition will play a huge part in the end result.  Good luck.