Early Entrance is only ever at one park at a time. This month it's for USF as opposed to IOA.
In terms of how early to get to the gate next week to try and do Hagrid's first, it's tough to say because no one knows how busy it will be for the new ride. But many are expecting it will be quite busy. I would say to get to the gates at least an hour early (if not more). They may start letting people in early (to clear the crowds at the gates) and then have people queue up in Lost Continent (near the entrance of Hogsmeade).
But no one know for certain as of yet. But they have announced that if things are too crazy they will be using a "virtual line" on the app to help keep Hogsmeade less crowded if the lines extend beyond the actual ride queue and into Hogsmeade.