Peter first power, before his very own power, was to dream timed events (be them past, present or future) more specially future events, and clearly got that from Angela (she even told that to Peter this season)
I might be missing something, but what is this about Peter having Linderman's power?, I haven't seen him used that power on the show, ever.
he didn't heal Nathan, at least he didn't do it on purpose, since he wanted Nathan dead... at least until he's sure he's not going to tell anybody about their powers, which was what Peter came to stop
Linderman is dead... it seems, since the only one able to see him is Nathan...
though there will a scene in which Linderman
Spoiler:
talks or interacts with Daphne
so the whole truth about Linderman hasn't been revealed yet
btw: I like having McDowell back in the show....