@FredMSloniker
Targets have to be legal when chosen, so no one can choose a permanent with, say, shroud. (Funnily enough, while your opponents may choose the targets for this ability, you always control the ability itself, so hexproof and ward don’t impede the choice.)

As long as your entire board doesn’t have shroud, protection from blue, or something else that makes every option illegal, you’re getting something out of Interplanar Parallels each time it resolves… unless someone makes the target illegal in response. This could mean giving it one of the above abilities, or they could just kill it. “Pick something, then kill it first” is definitely a viable line, assuming they have a kill spell handy and don’t mind using it then and there.

So, if I understand this correctly, when you planeswalk, you choose one of your nonlegendary, nonland permanents and create a token copy. When someone else planeswalks, they choose one of your nonlegendary, nonland permanents, but you create (and control) the token copy. And in both cases, since it says ‘target’, the choice has to be a valid target. Is there ever a situation where you can’t target one of your own permanents? Can they choose something they can’t target and cause nothing to happen, or must they choose something they can target if able?