Can I walk across the bridge? If so, where is the entrance to gain access?

You can walk across, but only the north side walk is open. On the Highland side there is a park w/ parking that's accessible to the bridge. Not sure about the Poughkeepsie side.

There us street parking on the Poughkeepsie side.

Yes, you can walk across on the Poughkeepsie side obviously. There is parking at the train station or on Rinaldi Blvd. There are maps by the walkway that show the loop you can walk across the walkway, through the D'iorio park in Highland to the Midhudson bridge & across, then the route back thru Poughkeepsie over to the walkway entrance