I think that what you're talking about in your first paragraph is so rare that I really can't give a strong opinion one way or another. If they wanted to award the team a faceoff in the offensive zone, fine with me. If they didn't want to make it reviewable, fine with me. In my eyes, they've already completely killed the play. That sucks, but I don't see any real way to correct it.
In terms of challenging penalties, my answer is what it has been for the last number of posts. What is and what is not a penalty shifts based on who is making the determination. And that remains true to some degree regardless of training. Humans are not uniform in their interpretations of identically viewed events. But, for something like offside, there is a quantifiable boundary that limits the range of interpretation. The question is the same, with the same limits, for everyone viewing it. Did the player enter the zone prior to the puck?
Let's talk about the goalie interference rule for a second. A subjective (no set boundaries) review. When coaches first began challening for GI, I swear than I was 95% or above on determining the call after review based on replay. Now? I maybe get it right 3 out of every 4 times. I can't pinpoint exactly why my winning percentage on these calls seems to be dipping, but I can tell you a very big reason that I'm often caught off-guard by what the refs rule. Because, even with a rulebook full of apparent "boundaries", there is subjectivity in such a call. There is no physical line saying, "this is goalie interference, that is not". Do I want reviews on GI out of the game? No, only because it is IMMEDIATE event prior to a goal. But for other events of subjectivity? You'd have endless interpretations varying from minute-to-minute, game-to-game. It would be downright impossible to truly create consistency.
What you start getting into in reviewing penalties is introducing the frustration of goalie interference calls all over the ice. For that reason, I am opposed to it.