Question on biking and when the park is “open”?

I’m thinking of going to GNP for 2-4 days in late May or early June when it’s closed to cars. Can someone clarify what that means exactly? Is the whole park closed to cars as in you can’t even enter the park via a vehicle? Or, can you drive to say Apgar, leave your car and bike rack, and then bike around the rest of the park?

Similarly, are visitor’s centers open before early June? Or is it a situation where rangers exist, but everyone’s kind of on their own?

The idea of biking to the park everyday to then do the roads out there is treacherous from a mileage perspective. Being able to drive beyond the entrance and hopefully to Apgar seems much more manageable.