The token created by Adagia’s last ability copies exactly what was printed on the original permanent and nothing else, with the listed exception (unless that permanent is copying something else or is a token; see below). It doesn’t copy whether that permanent is tapped or untapped, whether it has any counters on it or Auras and Equipment attached to it, or any non-copy effects that have changed its power, toughness, types, color, or so on. If it is a Vehicle, it is not crewed. If it is an Equipment, it is not attached to any creature.