The top material will depend on the type of frog kept. If Darts or Mantellas you will need very high humidity and the top will be glass or plexi with little venting. As an example, my ExoTerras have a solid pane of glass covering the whole top. Now if you keep frogs that require lower humidity levels; a screen or partial screen top would be the way to go.

If a heater for water section is required; you can use a submersible type aquarium heater. It must be matched to the actual water volume in the enclosure and kept submerged at all times. A heat mat would be located on the side and away from water feature. That glass pane will get hot and splashing water on it could be a problem.

Is there a particular reason why your false bottom can't exceed 2 in. height? Seems to me a 150G tank could easily have a much deeper false bottom .