Regarding a mens mikvah:
In a mikvah where there are no divisions between the changing room and the actual Mikvah - would one be able to say a pasuk in the Mikvah if no one else is in the changing room or Mikvah.
Answer:
No, it is forbidden to recite a pasuk in a place where the way of people is to be naked. See Mishnah Berurah 84:3.