Would it be okay to add unlockables that are only visual - like a trophy shelf, that changes nothing gameplay wise, but are unlocked upon replays and only stay for the duration of the session?

Also, would it be okay to add a total counter that adds actions from all playthroughs in the same session, that would say something along the lines of "You did X action 200 times this session!"?

I'm also planning for an easy/med/hard mode but i believe that's well within the rules. 

Ideally, no unlockables because it's a form of progression that extends the game

Stats are OK so your action counter sounds fine to me

Difficulty modes are also fine