If i went to the bathroom, took a shower, cut my nails and cut my hair, how many times do i need to wash my hands

The purpose for washing of the hands in the instances mentioned is because a "bad spirit" rests upon the hands or so the hands are clean for the study of torah or Tefilla. Once the hands are washed there is no more bad spirit and the hands are clean. Therefore if all the above actions were done consecutively, washing them one time is sufficient. . (See Shulchan aruch Orach Chaim 4:18)