Those are some cool ideas, but...
1. How would Spy work though? He would just say who are the imposters and everyone will kill the imposters and gg.
2. If Medic will heal the dead body, then the guy that was healed can just tell who is the imposter right away. I know you said he can't do that, but I don't think it will be possible to do so in an actual game.
3. Running should be available to both crewmates and imposters, so it won't be possible to just run and prove that you're crewmate (though maybe there can be an option that makes it so imposters have longer cooldown for running, but it still can be used to know who is crewmate and who is imposter)