The answer to these questions depends on information you're not giving in your hypotheticals. For instance:
>"Am I violating a contract by getting in your car and driving it away? ... Have I initiated force in any of these cases? Are there rights that are granted when I haven't explicitly signed a contract?"
I don't know. Did you just sign a rental agreement with me where I give you the right to use the car in exchange for the payment you just gave me? Or are you someone I've never met whose stealing my car?
If we had a society that was just when it comes to the really obvious issues-- like, rape, murder, theft, etc, then we could debate the morality of you singing a son (I'm assuming your hypothetical is singing a song that is copyrighted by someone else, but in my society there would be no implicit copyright.)
I'm not trying to evade. IF you steal my car, it is an initiation of force. If you walk into my house when you don't have permission, its an initiation, whether the door was unlocked or not.
>"and if it is, what if you lack the size to prevent me from doing it?"
I'm addressing the moral question of whether its an imitation or not. The practical question of how to defend against such initiations is a broader topic.
"Is there an involuntary limit to what can be signed away?"
That's also a good topic for debate.
I'd like to start, though, by focusing on the obvious initiations of force-- groups of people using violence to take from others, and groups of people waging wars on the innocent, or incarcerating people for doing drugs, etc.
The NAP doesn't imply there are no grey areas at all-- there are grey areas.
But the NAP does let you see that a lot of areas that people think are white are actually black. That the war on drugs is not only ill advised, but a criminal enterprise.