If I am staying on site and have general admission (2 park) tickets on a day that HHN happens, will I have to leave the park when HHN starts or can I still access parts of the park?
I think you’ll have to leave US, but IOA would be open to you.
You will be excited from the Studios at 5:00. Up till then you can experience anything you’d like.
One thing that closes early is Hogwarts Express. It’s timed so the last train from Studios runs at 5:00pm, so they close the line early. The last train from IoA is timed to arrive at Studios before 5:00, so that closes even earlier.
Also, beginning at 5:00 at Studios there will be lines of security posted at various places, and they will not let anyone past that point.